40s applied prob questions 2012-2013

40s app prob questions

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Which expression correctly describes the experimental probability, P ( B ), where n ( B ) is the number of times event B occurred and n ( T ) is the total number of trials, T , in the experiment?

A.

B.

C.

D.

____ 2. Which expression correctly describes the theoretically probability, P ( X ), where n ( X ) is the number of times event X occurred and n ( S ) is the number of outcomes in the sample space, S , where all outcomes are equally likely?

A.

B.

C.

D.

____ 3. Given the following probabilities, which event is most likely to occur?

A.

P ( A ) = 0.2

B.

P ( B ) =

C.

P ( C ) = 0.3

D.

P ( D ) =

____ 4. Given the following probabilities, which event is most likely to occur?

A.

P ( A ) = 0.28

B.

P ( B ) =

C.

P ( C ) = 0.27

D.

P ( D ) =

____ 5. Three events, A , B , and C , are all equally likely. If there are no other possible events, which of the following statements is true?

A.

P ( A ) = 0

B.

P ( B ) =

C.

P ( C ) = 1

D.

P ( A ) = 3

____ 6.

The odds of Macy passing her driver’s test on the first try are 7 : 4. Determine the odds against

Macy passing her driver’s test.

A.

4 : 7

B.

4 : 11

C.

7 : 11

D.

3 : 11

____ 7. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls out a coin at random. Determine the odds against the coin being a quarter.

A.

1 : 4

B.

1 : 3

C.

3 : 4

D.

3 : 1

____ 8. Julie draws a card at random from a standard deck of 52 playing cards. Determine the odds in favour of the card being a heart.

A.

3 : 1

B.

1 : 3

C.

1 : 1

D.

3 : 13

____ 9. Tia notices that yogurt is on sale at a local grocery store. The last eight times that yogurt was on sale, it was available only three times. Determine the odds against yogurt being available this time.

A.

3 : 5

B.

3 : 8

C.

5 : 8

D.

5 : 3

____ 10. Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the wall 7 times in 28 attempts. Determine the odds against Zahra climbing to the top.

A.

3 : 1

B.

4 : 1

C.

3 : 11

D.

3 : 4

____ 11.

The odds of Macy passing her driver’s test on the first try are 7 : 4. Determine the probability that she will pass her driver’s test.

A.

0.226

B.

0.364

C.

0.571

D.

0.636

____ 12. Raymond has 12 coins in his pocket, and 9 of these coins are quarters. He reaches into his pocket and pulls out a coin at random. Determine the probability of the coin being a quarter.

A.

0.250

B.

0.333

C.

0.750

D.

0.848

____ 13. Julie draws a card at random from a standard deck of 52 playing cards. Determine the probability of the card being a diamond.

A.

0.250

B.

0.500

C.

0.625

D.

0.750

____ 14. Tia notices that yogurt is on sale at a local grocery store. The last eight times that yogurt was on sale it was available only three times. Determine the probability of yogurt being available this time.

A.

0.220

B.

0.375

C.

0.460

D.

0.625

____ 15. Zahra likes to go rock climbing with her friends. In the past, Zahra has climbed to the top of the wall 7 times in 28 attempts. Determine the probability of Zahra climbing to the top this time.

A.

0.250

B.

0.333

C.

0.625

D.

0.750

____ 16. The weather forecaster says that there is an 80% probability of rain tomorrow. Determine the odds against rain.

A.

4 : 5

B.

4 : 1

C.

1 : 5

D.

1 : 4

____ 17. The weather forecaster says that there is a 30% probability of fog tomorrow. Determine the odds against fog.

A.

3 : 7

B.

3 : 10

C.

7 : 3

D.

7 : 10

____ 18. The weather forecaster says that there is a 50% probability of showers tomorrow. Determine the odds against showers.

A.

1 : 1

B.

5 : 10

C.

2 : 1

D.

1 : 2

____ 19. A sports forecaster says that there is a 75% probability of a team winning their next game.

Determine the odds against that team winning their next game.

A.

3 : 4

B.

1 : 3

C.

3 : 1

D.

1 : 4

____ 20. A sports forecaster says that there is a 40% probability of a team winning their next game.

Determine the odds against that team winning their next game.

A.

2 : 3

B.

2 : 5

C.

3 : 5

D.

3 : 2

____ 21. A credit card company randomly generates temporary three-digit pass codes for cardholders. The pass code will consist of three different even digits. Determine the total number of pass codes using three different even digits.

A.

5

P

5

B.

5

P

3

C.

5

P

4

D.

5

P

1

____ 22. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary. Determine the number of ways in which these 2 people can be chosen for president and secretary.

A.

2

P

2

B.

2

P

1

C.

18

P

2

D.

18

P

16

____ 23. Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the number of options where at least one coin lands as heads.

A.

1

B.

3

C.

5

D.

7

____ 24. A credit card company randomly generates temporary four-digit pass codes for cardholders.

Determine the number of four digit pass codes.

A.

10

B.

100

C.

1000

D.

10 000

____ 25. From a committee of 18 people, 2 of these people are randomly chosen to be president and secretary. Determine the total number of possible committees.

A.

18

P

16

B.

18

P

4

C.

18

P

2

D.

18

P

12

____ 26. Yvonne tosses three coins. She is calculating the probability that at least one coin will land as heads. Determine the total number of outcomes.

A.

2

B.

4

C.

8

D.

16

____ 27. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the probability that only boys will be on the trip.

A.

0.02%

B.

0.08%

C.

0.15%

D.

0.23%

____ 28. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the probability that there will be equal numbers of boys and girls on the trip.

A.

17.23%

B.

22.61%

C.

27.35%

D.

34.06%

____ 29. Nine boys and twelve girls have signed up for a trip. Only six students will be selected to go on the trip. Determine the number of ways in which there can be more girls than boys on the trip.

A.

17 456

B.

25 872

C.

29 778

D.

35 910

____ 30. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the van. Determine the probability that only boys will be sitting at the front.

A.

28.57%

B.

33.45%

C.

39.06%

D.

46.91%

____ 31. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the van. Determine the probability that there will be equal numbers of boys and girls sitting at the front.

A.

53.07%

B.

57.14%

C.

59.36%

D.

62.23%

____ 32. Four boys and three girls will be riding in a van. Only two people will be selected to sit at the front of the van. Determine the number of ways in which there can be more girls than boys sitting at the front.

A.

3

B.

4

C.

5

D.

6

____ 33. Yvonne tosses three coins. Determine the probability that at least one coin will land as heads.

A.

12.5%

B.

37.5%

C.

62.5%

D.

87.5%

____ 34. Cai tosses four coins. Determine the probability that they are all tails.

A.

6.25%

B.

12.50%

C.

18.75%

D.

25.00%

____ 35. Dora tosses four coins. Determine the probability that at least two coins will land as heads.

A.

37.52%

B.

46.30%

C.

68.75%

D.

74.17%

____ 36. Jake and Agnes are playing a board game. If a player rolls a sum greater than 9 or a multiple of 6, the player gets a bonus of 50 points. Determine the probability of rolling a sum greater than 9.

A.

B.

C.

D.

____ 37. Jake and Agnes are playing a board game. If a player rolls a sum greater than 9 or a multiple of 6, the player gets a bonus of 50 points. Determine the probability of rolling a multiple of 6.

A.

B.

C.

D.

____ 38. Two dice are rolled. Let A represent rolling a sum greater than 7. Let B represent rolling a sum that is a multiple of 3. Determine n ( A



B ).

A.

5

B.

8

C.

12

D.

15

____ 39. Two dice are rolled. Let A represent rolling a sum greater than 10. Let B represent rolling a sum that is a multiple of 2. Determine n ( A



B ).

A.

1

B.

3

C.

11

D.

18

____ 40. Two dice are rolled. Let A represent rolling a sum greater than 6. Let B represent rolling a sum that is a multiple of 4. Determine P ( A



B ).

A.

B.

C.

D.

____ 41. Two dice are rolled. Let A represent rolling a sum greater than 8. Let B represent rolling a sum that is a multiple of 3. Determine P ( A



B ).

A.

B.

C.

D.

____ 42. Select the events that are mutually exclusive.

A. Drawing a 7 or drawing a heart from a standard deck of 52 playing cards.

B. Rolling a sum of 4 or rolling an even number with a pair of four-sided dice, numbered 1 to 4.

C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards.

D. Rolling a sum of 8 or a sum of 11 with a pair of six-sided dice, numbered 1 to 6.


A. Drawing a red card or drawing a diamond from a standard deck of 52 playing cards.

B. Rolling a sum of 8 or rolling an even number with a pair of six-sided dice, numbered 1 to 6.

C. Drawing a black card or drawing a Queen from a standard deck of 52 playing cards.

D. Drawing a 3 or drawing an even card from a standard deck of 52 playing cards.


A. Rolling a sum of 9 or rolling a multiple of 3 with a pair of six-sided dice, numbered 1 to 6.

B. Drawing a Jack or drawing a face card from a standard deck of 52 playing cards.

C. Walking to school or taking the bus to school.

D. Drawing a 2 or drawing a spade from a standard deck of 52 playing cards.

____ 45. Josie is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a red card or a 7.

A.

B.

C.

D.

____ 46. Helen is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a black card or a spade.

A.

B.

C.

D.

____ 47. Roena is about to draw a card at random from a standard deck of 52 playing cards. Determine the probability that she will draw a heart or a King.

A.

B.

C.

D.

____ 48. Samuel rolls two regular six-sided dice. Determine the odds against him rolling an even sum or an

8.

A.

1 : 3

B.

25 : 11

C.

21 : 15

D.

1 : 1

____ 49. Rashid rolls two regular six-sided dice. Determine the odds against him rolling a sum of 6 or a sum of 9.

A.

5 : 1

B.

3 : 1

C.

25 : 11

D.

2 : 1

____ 50. Lorne rolls two regular six-sided dice. Determine the odds against him rolling an odd sum or a 4.

A.

7 : 11

B.

1 : 8

C.

17 : 19

D.

5 : 7

____ 51. Julio rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 3 and the sum of the two dice is greater than 5, Julio wins a point. Determine the probability that Julio will win a point.

A.

B.

C.

D.

____ 52. Brian rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 5 and the sum of the two dice is greater than 9, Brian wins a point. Determine the probability that

Brian will win a point.

A.

B.

C.

D.

____ 53. Hilary draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine the probability that both cards are hearts.

A.

B.

C.

D.

____ 54. Sarah draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine the probability that both cards are NOT face cards.

A.

B.

C.

D.

____ 55. Min draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are face cards.

A.

B.

C.

D.

____ 56. Misha draws a card from a well-shuffled standard deck of 52 playing cards. Then he puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are even numbers.

A.

B.

C.

D.

____ 57. Select the events that are dependent.

A. Drawing a face card from a standard deck of 52 playing cards, putting it back, and then drawing another face card.

B. Rolling a 4 and rolling a 3 with a pair of six-sided dice, numbered 1 to 6.

C. Drawing a heart from a standard deck of 52 playing cards, putting it back, and then drawing another heart.

D. Rolling a 3 and having a sum greater than 5 with a pair of six-sided dice, numbered

1 to 6.

____ 58. Select the events that are dependent.

A. Rolling a 2 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6.

B. Drawing an odd card from a standard deck of 52 playing cards, putting it back, and then drawing another odd card.

C. Drawing a spade from a standard deck of 52 playing cards and then drawing another spade, without replacing the first card.

D. Rolling an even number and rolling an odd number with a pair of six-sided dice, numbered 1 to 6.

____ 59. Select the events that are independent.

A. Choosing a number between 1 and 30 with the number being a multiple of 2 and also a multiple of 4.

B. Drawing a heart from a standard deck of 52 playing cards and then drawing another heart, without replacing the first card.

C. Rolling a 2 and having a sum greater than 4 with a pair of six-sided dice, numbered

1 to 6.

D. Rolling a 1 and rolling a 6 with a pair of six-sided dice, numbered 1 to 6.

____ 60. Select the events that are independent.

A. Drawing a 10 from a standard deck of 52 playing cards and then drawing another card, without replacing the first card.

B. Rolling a 4 and rolling a 5 with a pair of six-sided dice, numbered 1 to 6.

C. Choosing a number between 1 and 20 with the number being a multiple of 3 and also a multiple of 9.

D. Drawing a diamond from a standard deck of 52 playing cards and then drawing another diamond, without replacing the first card.

____ 61. There are 40 males and 60 females in a graduating class. Of these students, 10 males and

20 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.

A.

0.3

B.

0.4

C.

0.5

D.

0.6

____ 62. There are 60 males and 90 females in a graduating class. Of these students, 30 males and

50 females plan to attend a certain university next year. Determine the probability that a randomly selected student plans to attend the university.

A.

0.41

B.

0.47

C.

0.53

D.

0.59

____ 63. Rino has six loonies, four toonies, and two quarters in his pocket. He needs two loonies for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are loonies.

A.

16.3%

B.

18.4%

C.

22.7%

D.

25.9%

____ 64. Paul has four loonies, three toonies, and five quarters in his pocket. He needs two quarters for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are quarters.

A.

15.15%

B.

19.64%

C.

26.47%

D.

32.13%

____ 65. Anthony has three loonies, four toonies, and seven quarters in his pocket. He needs two toonies for a parking meter. He reaches into his pocket and pulls out two coins at random. Determine the probability that both coins are toonies.

A.

2.1%

B.

6.6%

C.

9.2%

D.

12.7%

____ 66. Rashid goes to the gym and does two different cardio workouts each day. His choices include using a treadmill, a stepper, a stationary bike, an elliptical walker, and running the track.

Determine the probability that the next time Rashid goes to the gym he will use the stepper and then run the track.

A.

1%

B.

5%

C.

8%

D.

14%

____ 67. Carlo goes to the gym and does two different cardio workouts each day. His choices include using a treadmill, a stationary bike, and running the track. Determine the probability that the next time

Carlo goes to the gym will use the stationary bike and then run the track.

A.

16.7%

B.

26.1%

C.

33.4%

D.

41.9%

____ 68. A three-colour spinner is spun, and a die is rolled. Determine the probability that you spin blue and roll a 4.

A.

1.24%

B.

5.56%

C.

7.17%

D.

9.82%

____ 69. A five-colour spinner is spun, and a die is rolled. Determine the probability that you spin yellow and roll a 6.

A.

2.42%

B.

3.33%

C.

6.13%

D.

7.75%

____ 70. A four-sided red die and a six-sided green die are rolled. Determine the probability of rolling a 2 on the red die and a 5 on the green die.

A.

4.17%

B.

4.89%

C.

6.50%

D.

8.04%

____ 71. A four-sided red die and a four-sided green die are rolled. Determine the probability of rolling a 1 on the red die and rolling a 3 on the green die.

A.

0.23%

B.

3.09%

C.

6.25%

D.

10.16%

____ 72. Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the probability of drawing a five then drawing a two.

A.

0.603%

B.

1.227%

C.

1.613%

D.

2.009%

____ 73. Two cards are drawn, without being replaced, from a standard deck of 52 playing cards. Determine the probability of drawing a face card then drawing an even-numbered card.

A.

1.96%

B.

9.05%

C.

14.32%

D.

23.08%

____ 74. There are 20 cards, numbered 1 to 20, in a box. Two cards are drawn, one at a time, with replacement. Determine the probability of drawing an even number then drawing a number that is a multiple of 4.

A.

8.8%

B.

9.3%

C.

10.7%

D.

12.5%

____ 75. There are 35 cards, numbered 1 to 35, in a box. Two cards are drawn, one at a time, with replacement. Determine the probability of drawing two multiples of 10.

A.

0.02%

B.

0.36%

C.

0.73%

D.

0.99%

____ 76. Select the independent events.

A. P ( A ) = 0.22, P ( B ) = 0.39, and P ( A



B ) = 0.072

B. P ( A ) = 0.18, P ( B ) = 0.7, and P ( A



B ) = 0.163

C. P ( A ) = 0.51, P ( B ) = 0.1, and P ( A



B ) = 0.069

D. P ( A ) = 0.9, P ( B ) = 0.23, and P ( A



B ) = 0.207


A. P ( A ) = 0.67, P ( B ) = 0.12, and P ( A



B ) = 0.086

B. P ( A ) = 0.83, P ( B ) = 0.4, and P ( A



B ) = 0.378

C. P ( A ) = 0.4, P ( B ) = 0.91, and P ( A



B ) = 0.364

D. P ( A ) = 0.2, P ( B ) = 0.32, and P ( A



B ) = 0.046


A. P ( A ) = 0.21, P ( B ) = 0.57, and P ( A



B ) = 0.122

B. P ( A ) = 0.8, P ( B ) = 0.52, and P ( A



B ) = 0.423

C. P ( A ) = 0.74, P ( B ) = 0.85, and P ( A



B ) = 0.629

D. P ( A ) = 0.46, P ( B ) = 0.9, and P ( A



B ) = 0.416

____ 79. There are three children in the Jaffna family. Determine the probability that they have two boys and a girl.

A.

12.5%

B.

25%

C.

37.5%

D.

50%

____ 80. There are three children in the Stribling family. Determine the probability that all the children are girls.

A.

12.5%

B.

25%

C.

37.5%

D.

50%

Short Answer

1. Jean and Kira have invented a game:

• Two people play.

• For each turn, both players roll a die.

- Player 1 scores a point in the sum of the two numbers is even.

- Player 2 scores a point in the sum of the two numbers is odd.

• A game consists of 10 turns.

Is their game fair? If it is not fair, which player has the advantage?

2. Jason and Coulter have invented a game:

• Two people play.

• For each turn, both players roll a die.

- Player 1 scores a point in the product of the two numbers is even.

- Player 2 scores a point in the product of the two numbers is odd.

• A game consists of 10 turns.

Is their game fair? If it is not fair, which player has the advantage?

3. Three events, A , B , C , D , and E , are all equally likely. If there are no other possible events, what is the probability of event B ?

4. A game has three possible outcomes: A , B , and C . If P ( A ) = 0.6 and P ( B ) = 0.2, what is the probability of event C ?

5. A game has four possible outcomes: A , B , C , and D . If P ( A ) = 0.4, P ( B ) = 0.1, and P ( C ) = P ( D ), what is the probability of event C ?

6. Jessica rolls a standard die. Determine the probability of her rolling a 2.

7. Salim draws a card at random from a standard deck of 52 playing cards. Determine the probability of the card being black.

8. Denis has 15 coins in his pocket, and 6 of them are toonies. He reaches into his pocket and pulls out a coin at random. Determine the probability of the coin being a toonie.

9. Teresa notices that bagels are on sale at a local grocery store. The last four times that bagels were on sale, they were available only once. Determine the odds in favour of bagels being available this time.

10. Matias likes to go skiing with his friends. In the past, Matias has made it to the bottom of the hill without falling 18 times in 45 attempts. Determine the odds against Matias making it to the bottom without falling this time.

11. Elise rolls a standard die. Determine the odds against her rolling an even number.

12. Josephine plays ringette. She has scored 3 times in 15 shots on goal. She says that the odds in favour of her scoring are 1 to 5. Is she right? Explain.

13. Mark plays basketball. He has scored 6 times in 8 shots on basket. He says the odds in favour of him scoring are 3 : 4. Is he right? Explain.

14. Ned plays hockey. He has scored 5 times out of 25 shots on goal. He says the odds in favour of him scoring are 1 : 5. Is he right? Explain.

15. Brian has been awarded a penalty shot in a hockey game. Colby is the goalie. Brian has scored 4 times in his last 10 penalty shots. Colby has blocked 7 of the last 10 penalty shots. Determine the odds in favour of Brian scoring, using his data.

16. Jeff has been awarded a penalty shot in a hockey game. Braden is the goalie. Jeff has scored 6 times in his last 10 penalty shots. Braden has blocked 5 of the last 10 penalty shots. Determine the odds in favour of Jeff scoring, using his data.

17. Brian has been awarded a penalty shot in a hockey game. Colby is the goalie. Brian has scored 4 times in his last 10 penalty shots. Colby has blocked 7 of the last 10 penalty shots. Determine the odds in favour of Brian scoring, using Colby’s data.

18. Jeff has been awarded a penalty shot in a hockey game. Braden is the goalie. Jeff has scored 6 times in his last 10 penalty shots. Braden has blocked 5 of the last 10 penalty shots. Determine the odds in favour of Jeff scoring, using Braden’s data.

19. The coach of a basketball team claims that, for the next game, the odds in favour of the team winning are 5 : 3, the odds in favour of the team losing are 1 : 3, and the odds against a tie are 7 :

1. Are these odds possible? Explain.

20. The coach of a basketball team claims that, for the next game, the odds in favour of the team winning are 7 : 3, the odds in favour of the team losing are 1 : 9, and the odds against a tie are 4 :

1. Are these odds possible? Explain.

21. A credit card company randomly generates temporary four-digit pass codes for cardholders. Serena is expecting her credit card to arrive in the mail. Determine the probability that her pass code will consist of four different odd digits.

22. A credit card company randomly generates temporary five-digit pass codes for cardholders.

Meghan is expecting her credit card to arrive in the mail. Determine, to the nearest hundredth of a percent, the probability that her pass code will consist of five different even digits.

23. From a committee of 12 people, 3 of these people are randomly chosen to be president, vicepresident, and secretary. Determine, to the nearest hundredth of a percent, the probability that

Pavel, Rashida, and Jerry will be chosen.

24. From a committee of 18 people, 3 of these people are randomly chosen to be president, vicepresident, and secretary. Determine, to the nearest hundredth of a percent, the probability that

Evan, Elise, and Jaime will be chosen.

25. Access to a particular online game is password protected. Every player must create a password that consists of three capital letters followed by two digits. Repetitions are NOT allowed in a password.

Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters J, K, and L.

26. Access to a particular online game is password protected. Every player must create a password that consists of three capital letters followed by two digits. Repetitions are allowed in a password.

Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters A, D, and T.

27. Access to a particular online game is password protected. Every player must create a password that consists of four capital letters followed by three digits. Repetitions are NOT allowed in a password. Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters E, J, M, and T.

28. Access to a particular online game is password protected. Every player must create a password that consists of four capital letters followed by three digits. Repetitions are allowed in a password.

Determine, to the nearest thousandth of a percent, the probability that a password chosen at random will contain the letters A, E, I, and O.

29. Simone needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that her password will be greater than 3500.

30. Abigail needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that her password will be greater than 6300.

31. Denise needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest tenth of a percent, the probability that her password will be greater than 2250.

32. Veata needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine the probability that the first digit of her password will be 7.

33. Abigail needs to create a four-digit password to access her voice mail. She can repeat some of the digits, but all four digits cannot be the same. Determine, to the nearest percent, the probability that the first digit of her password will be even and the third digit will be odd.

34. Ashley has letter tiles that spell NAPKIN. She has selected three of these tiles at random.

Determine the probability that the tiles she selected are two consonants and one vowel.

35. Sonja has letter tiles that spell MICROWAVE. She has selected four of these tiles at random.

Determine, to the nearest tenth of a percent, the probability that the tiles she selected are two consonants and two vowels.

36. State whether the following events are mutually exclusive and explain your reasoning. Selecting a prime number or selecting an even number from a set of 10 balls, numbered 1 to 10.

37. State whether the following events are mutually exclusive and explain your reasoning. Rolling a sum of 5 or a sum of 9 with a pair of six-sided dice, numbered 1 to 6.

38. State whether the following events are mutually exclusive and explain your reasoning. Drawing a heart or drawing a Jack from a standard deck of 52 playing cards.

39. Brett is playing a board game. He must roll two four-sided dice, numbered 1 to 4. He can move if he rolls a sum of 4 (event A ) or a sum of 6 (event B ). Draw a Venn diagram to represent the two events.

40. Luke is playing a board game. He must roll doubles (event A ) or a sum of 6 (event B ). Draw a

Venn diagram to represent the two events.

41. Brandon is playing a board game. He must roll two four-sided dice, numbered 1 to 4. Determine the probability that Brandon will roll a sum of 5 or a sum of 7.

42. Brent is playing a board game. He must roll two four-sided dice, numbered 1 to 4. Determine the probability that Brent will roll a sum of 5 or 6.

43. Brittany rolls two six-sided dice, numbered 1 to 6. Determine the probability that she rolls an odd sum or a sum of 7.

44. Leanne rolls two six-sided dice, numbered 1 to 6. Determine the probability that she rolls a sum greater than 9 or a multiple of 4.

45. Jasmine is about to draw a card at random from a standard deck of 52 playing cards. If she draws an even number or a heart, she will win a point. Draw a Venn diagram to represent the two events.

46. Teresa is about to draw a card at random from a standard deck of 52 playing cards. If she draws a red card or a face card, she will win a point. Draw a Venn diagram to represent the two events.

47. The probability that Eva will go to the gym on Saturday is 0.63. The probability that she will go shopping on Saturday is 0.5. The probability that she will do neither is 0.3. Determine the probability that Eva will do at least one of these activities on Saturday.

48. The probability that Randy will study on Friday night is 0.3. The probability that he will play video games on Friday night is 0.7. The probability that he will do at least one of these activities is 0.9.

Determine the probability that he will do both activities.

49. The probability that Haley will exercise on Sunday is 0.6. The probability that she will go shopping on Sunday is 0.5. The probability that she will do both is 0.3. Determine the probability that Haley will do at least one of these activities on Sunday.

50. The probability that Vince will study on Friday night is 0.6. The probability that he will go out for dinner is 0.8. The probability that he will do at least one of these activities is 0.8. Determine the probability that he will do both activities.

51. A regular six-sided red die and a regular six-sided black die are rolled. The red die lands on 3 and the sum of the two dice is greater than 8. Are the two events dependent or independent?

52. A heart is drawn from a well-shuffled standard deck of 52 playing cards. Another card is drawn from the deck without replacing the first card. Are the two events dependent or independent?

53. A face card is drawn from a well-shuffled standard deck of 52 playing cards. Another card is drawn from the deck after replacing the first card. Are the two events dependent or independent?

54. Matias rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 2 and the sum of the two dice is greater than 4, Matias wins a point. Determine, to the nearest tenth of a percent, the probability that Matias will win a point.

55. Bernie rolls a regular six-sided red die and a regular six-sided black die. If the red die lands on 5 and the sum of the two dice is greater than 8, Bernie wins a point. Determine, to the nearest tenth of a percent, the probability that Bernie will win a point.

56. Anneliese draws a card from a well-shuffled standard deck of 52 playing cards. Then she draws another card from the deck without replacing the first card. Determine, to the nearest tenth of a percent, the probability that both cards are red.

57. Cheryl draws a card from a well-shuffled standard deck of 52 playing cards. Then she puts the card back in the deck, shuffles again, and draws another card from the deck. Determine the probability that both cards are black.

58. Leslie has four identical black socks and six identical white socks loose in her drawer. She pulls out one sock at random and then another sock, without replacing the first sock. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of black socks.

59. Janelle has eight identical black socks and two identical white socks loose in her drawer. She pulls out one sock at random and then another sock, without replacing the first sock. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of white socks.

60. Bonita has six identical red marbles and ten identical blue marbles in a paper bag. She pulls out one marble at random and then another marble, without replacing the first marble. Determine the probability that she pulls out a pair of red marbles.

61. Jasmine has two identical red marbles and twelve identical blue marbles in a paper bag. She pulls out one marble at random and then another marble, without replacing the first marble. Determine, to the nearest tenth of a percent, the probability that she pulls out a pair of blue marbles.

62. A computer manufacturer knows that, in a box of 175 computer chips, 5 will be defective. Max will draw 2 chips at random, from a box of 175. Determine, to six decimal places, the probability that Max will draw 2 defective chips.

63. A computer manufacturer knows that, in a box of 175 computer chips, 5 will be defective. Max will draw 2 chips at random, from a box of 175. Determine, to the nearest thousandth, the probability that Max will draw 2 non-defective chips.

64. A computer manufacturer knows that, in a box of 100 computer chips, 2 will be defective. Eric will draw 2 chips at random, from a box of 100. Determine, to six decimal places, the probability that Eric will draw 2 defective chips.

65. A computer manufacturer knows that, in a box of 100 computer chips, 2 will be defective. Eric will draw 2 chips at random, from a box of 100. Determine, to the nearest thousandth, the probability that Eric will draw 2 non-defective chips.

66. A four-colour spinner is spun, and a four-sided die is rolled. Determine the probability of spinning

67. A five-colour spinner is spun, and a four-sided die is rolled. Determine the probability of spinning orange and rolling a 1.

green and rolling a 3.

Problem

68. A standard red die and a four-sided green die are rolled. Determine, to the nearest hundredth of a percent, the probability of rolling a 6 on the red die and a 2 on the green die.

69. Two cards are drawn without being replaced, from a standard deck of 52 playing cards. Determine, to the nearest hundredth of a percent, the probability of drawing an odd-numbered card (ace, 3, 5,

7, or 9) then a face card.

70. Two cards are drawn without being replaced, from a standard deck of 52 playing cards. Determine, to the nearest hundredth of a percent, the probability of drawing a spade and a diamond.

71. There are 15 cards, numbered 1 to 15, in a box. Two cards are drawn, one at a time, with replacement. Determine, to the nearest tenth of a percent, the probability of drawing a multiple of 2 then a multiple of 3.

72. A die is rolled twice. Determine the probability that the first roll is a 3 and the second roll is a 5.

73. A die is rolled twice. Determine the probability that the first roll is greater than 2, and the second roll is odd.

74. A die is rolled twice. Determine the probability that the first roll is greater than 5 and the second roll is less than 4.

75. A die is rolled twice. Determine the probability that the first roll is greater than 3, and the second roll is less than 3.

76. Two single-digit random numbers (0 to 9) are selected independently. Determine the probability that their sum is 7.

77. Two single-digit random numbers (0 to 9) are selected independently. Determine the probability that their sum is 5.

78. Suppose that P ( A ) = 0.4, P ( B ) = 0.2, and P ( A



B ) = 0.08. Are events A and B independent?

Explain.





Explain.





Explain.

1. A hockey game has ended in a tie after a 5 min overtime period, so the winner will be decided by a shootout. The coach must decide whether Jules or Vicki should go first in the shootout. The coach would prefer to use her best scorer first, so she will base her decision on the players’ shootout records.

Player

Jules

Attempts

15

Goals Scored

7

Vicki 19 12

Who should go first? Show your work.

2. A hockey game has ended in a tie after a 5 min overtime period, so the winner will be decided by a shootout. The coach must decide whether Leanne or Krysta should go first in the shootout. The coach would prefer to use her best scorer first, so she will base her decision on the players’ shootout records.

Player

Leanne

Attempts

12

Goals Scored

8

Krysta 14


9

3. A hockey game has ended in a tie after a 5 min overtime period, so the winner will be decided by a shootout. The coach must decide whether Beth or Sierra should go first in the shootout. The coach would prefer to use her best scorer first, so she will base her decision on the players’ shootout records.

Player Attempts Goals Scored

Beth 9 7

Sierra 13 8


4. A group of students are holding a charity carnival to support a local animal shelter. The students have created a dice game that they call Zim and a card game that they call Bap. The odds against winning Zim are 3 : 1, and the odds against winning Bap are 4 : 5. Which game should Sarah play?

Show your work.

5. A group of students are holding a charity carnival to support a local animal shelter. The students have created a dice game that they call Zing and a card game that they call Bloop. The odds against winning Zing are 3 : 2, and the odds against winning Bloop are 3 : 7. Which game should

Lena play? Show your work.

6. A group of students are holding a charity carnival to support a local animal shelter. The students have created a dice game that they call Boing and a card game that they call Zoop. The odds against winning Boing are 9 : 5, and the odds against winning Zoop are 7 : 2. Which game should

Sylvia play? Show your work.

7. A high-school football team has the ball at the opponent’s 2 yd line. It is the third down. The team is behind by 3 points, with only one second left in the game. The players have two options:



They can try to score a touchdown. In the past, they have succeeded 4 out of 10 times. If they score a touchdown, they will win the game.



They can try to kick a field goal. The kicker has scored a field goal from 20 yd or less in 7 out of 9 tries. If they score a field goal, they will get 3 points and tie the game forcing overtime. a) What are the odds in favour of each option? Show your work. b) Which option should the coach choose? Explain.

8. A high-school football team has the ball at the opponent’s 2 yd line. It is the third down. The team is behind by 3 points, with only one second left in the game. The players have two options:



They can try to score a touchdown. In the past, they have succeeded 8 out of 14 times. If they score a touchdown, they will win the game.



They can try to kick a field goal. The kicker has scored a field goal from 20 yd or less in 3 out of 5 tries. If they score a field goal, they will get 3 points and tie the game forcing overtime. a) What are the odds in favour of each option? Show your work. b) Which option should the coach choose? Explain.

9. Three people are running for president of the student council. The polls show Denis has a 55% chance of winning, Cyndi has a 25% chance of winning, and Chris has a 20% chance of winning. a) What are the odds in favour of each person winning? Show your work. b) Suppose that Chris withdraws and offers his support to Cyndi. Further suppose that his supporters also switch to Cyndi. What are the odds in favour of Cyndi winning now?

10. Three people are running for president of the student council. The polls show Jamal has a 40% chance of winning, Rebecca has a 35% chance of winning, and Henry has a 25% chance of winning. a) What are the odds in favour of each person winning? Show your work. b) Suppose that Henry withdraws and offers his support to Rebecca. Further suppose that his supporters also switch to Rebecca. What are the odds in favour of Rebecca winning now?

11.

Atian, Sam, Phuong, Mike, and Tariq are competing with ten other boys to be on their school’s cross-country team. All the boys have an equal chance of winning the trial race. Determine the probability that Atian, Sam, Phuong, Mike, and Tariq will place first, second, third, fourth, and fifth, in any order. Show your work.

12. Greg, Bogdan, Dave, and Li are competing with eight other boys to be on their school’s crosscountry team. All the boys have an equal chance of winning the trial race. Determine the probability that Greg, Bogdan, Dave, and Li will place first, second, third, and fourth in any order.

Show your work.

13. Conner hosts a morning radio show in Kenora. To advertise his show, he is holding a contest at a local mall. He spells out ONTARIO with letter tiles. Then he turns the tiles face down and mixes them up. He asks Gabe to arrange the tiles in a row and turn them face up. If the row of tiles spells

ONTARIO, Gabe will win a new car. Determine the probability that Gabe will win the car. Show your work.

14. Homer hosts a morning radio show in Halifax. To advertise his show, he is holding a contest at a local mall. He spells out NOVA SCOTIA with letter tiles. Then he turns the tiles face down and mixes them up. He asks Marie to arrange the tiles in a row and turn them face up. If the row of tiles spells NOVA SCOTIA, Marie will win a new car. Determine the probability that Marie will win the car. Show your work.

15. There are 20 bikes in a spinning class. The bikes are arranged in 4 rows, with 5 bikes in each row.

They hope to be in the same row, but they cannot request a specific bike. Determine the probability that all 5 friends will be in the same row, with Jeff and Dariya at either end. Show your work.

16. There are 12 bikes in a spinning class. The bikes are arranged in 4 rows, with 3 bikes in each row.

They hope to be in the same row, but they cannot request a specific bike. Determine the probability that all 3 friends will be in the same row, with Pia and Amy at either end. Show your work.

17. There are 11 players on a baseball team, all with roughly equal athletic ability. The coach has decided to choose the players who will play the four infield positions (first base, second base, third base, and shortstop) randomly. Tori and Brittany are on the team. Determine the odds in favour of

Tori and Brittany being chosen to play in the infield. Show your work.

18. There are 9 players on a baseball team, all with roughly equal athletic ability. The coach has decided to choose the players who will play the three outfield positions (left field, centre field, and right field) randomly. Tara and Katherine are on the team. Determine the odds in favour of Tara and Katherine being chosen to play in the outfield. Show your work.

19. A student council consists of 12 girls and 8 boys. To form a subcommittee, 4 students are randomly selected from the council. Determine the odds in favour of 3 girls and 1 boy being on the subcommittee. Show your work.

20. A student council consists of 10 girls and 9 boys. To form a subcommittee, 7 students are randomly selected from the council. Determine the odds in favour of 4 girls and 3 boys being on the subcommittee. Show your work.

21. A car manufacturer keeps a database of all the cars that are available for sale at all the dealerships in Western Canada. For model A, the database reports that 36% have heated leather seats, 41% have a sunroof, and 52% have neither. Determine the probability of a model A car at a dealership having both heated leather seats and a sunroof. Show your work.

22. A car manufacturer keeps a database of all the cars that are available for sale at all the dealerships in Western Canada. For model A, the database reports that 19% have heated leather seats, 39% have a sunroof, and 46% have neither. Determine the probability of a model A car at a dealership having both heated leather seats and a sunroof. Show your work.

23. A survey reported that 29% of households have one or more dogs, 35% have one or more cats, and

42% have neither dogs nor cats. Suppose that a household is selected at random. Determine the probability that there are cats but no dogs in the household. Show your work.

24. A survey reported that 42% of households have one or more dogs, 28% have one or more cats, and

39% have neither dogs nor cats. Suppose that a household is selected at random. Determine the probability that there are cats but no dogs in the household. Show your work.

25. Aisha plays the balloon pop game at a carnival. There are 50 balloons, with the name of a prize inside each balloon. The prizes are 10 stuffed bears, 6 toy trucks, 21 decks of cards, 9 yo-yos, and

4 giant stuffed dogs. Aisha pops a balloon with a dart. Determine the odds in favour of her winning either a stuffed dog or a stuffed bear. Show your work.

26. Madelaine plays the balloon pop game at a carnival. There are 35 balloons, with the name of a prize inside each balloon. The prizes are 8 stuffed tigers, 5 toy cars, 16 books, 4 boxes of crayons, and 2 giant stuffed pandas. Madelaine pops a balloon with a dart. Determine the odds in favour of her winning either a toy car or a book. Show your work.

27. Hiroko plays the balloon pop game at a carnival. There are 45 balloons, with the name of a prize inside each balloon. The prizes are 12 stuffed lions, 8 toy motorcycles, 16 decks of cards, 6 yo-yos, and 3 giant stuffed horses. Hiroko pops a balloon with a dart. Determine the odds in favour of her winning either a stuffed lion or a yo-yo. Show your work.

28. On Tuesday, the weather forecaster says that there is a 40% chance of snow on Wednesday and a

50% chance of snow on Thursday. The forecaster also says that there is a 10% chance of snow on both Wednesday and Thursday. Determine the probability that there will be snow on Wednesday or on Thursday. Show your work.

29. On Thursday, the weather forecaster says that there is a 40% chance of rain on Friday and a 70% chance of rain on Saturday. The forecaster also says that there is a 20% chance of rain on both

Friday and Saturday. Determine the probability that there will be rain on Friday or on Saturday.

Show your work.

30. On Sunday, the weather forecaster says that there is a 50% chance of freezing drizzle on Monday and a 30% chance of freezing drizzle on Tuesday. The forecaster also says that there is a 10% chance of freezing drizzle on both Monday and Tuesday. Determine the probability that there will be freezing drizzle on Monday or on Tuesday. Show your work.

31. Asha asks Tristan to choose a number between 1 and 20 and then say one fact about the number.

Tristan says that the number he chose is a multiple of 3. Determine the probability that the number is also a multiple of 2, using a Venn diagram. Show your work.

32. Sun asks Reese to choose a number between 1 and 35 and then say one fact about the number.

Reese says that the number he chose is a multiple of 4. Determine the probability that the number is also a multiple of 3, using a Venn diagram. Show your work.

33.

Debra is the coach of a junior ultimate team. Based on the team’s record, it has a 70% chance of winning on calm days and a 50% chance of winning on windy days. Tomorrow, there is a 30% chance of high winds. There are no ties in ultimate. What is the probability that Debra’s team will win tomorrow? Show your work.

34.

Rowan is the coach of a junior ultimate team. Based on the team’s record, it has a 80% chance of winning on calm days and a 60% chance of winning on windy days. Tomorrow, there is a 60% chance of high winds. There are no ties in ultimate. What is the probability that Rowan’s team will win tomorrow? Show your work.

35. Each day, Julia’s math teacher gives the class a warm-up question. It is a true-false question 20% of the time and a multiple-choice question 80% of the time. Julia gets 70% of the true-false questions correct, and 90% of the multiple-choice questions correct. Julia answers today’s question correctly. What is the probability that it was a multiple-choice question? Show your work.

36.

Each day, Tovah’s math teacher gives the class a warm-up question. It is a true-false question 40% of the time and a multiple-choice question 60% of the time. Tovah gets 70% of the true-false questions correct, and 80% of the multiple-choice questions correct. Tovah answers today’s question correctly. What is the probability that it was a multiple-choice question? Show your work.

37. Mena remembers to set her alarm clock 71% of the time. When she does remember to set her alarm clock, the probability that she will be late for school is 0.10. When she does not remember to set it, the probability that she will be late for school is 0.80. Mena was late today. What is the probability that she remembered to set her alarm clock? Show your work.

38. Trista remembers to set her alarm clock 82% of the time. When she does remember to set her alarm clock, the probability that she will be late for school is 0.30. When she does not remember to set it, the probability that she will be late for school is 0.60. Trista was late today. What is the probability that she remembered to set her alarm clock? Show your work.

39. The probability that a plane will leave Winnipeg on time is 0.80. The probability that a plane will leave Winnipeg on time and arrive in Calgary on time is 0.42. Determine the probability that a plane will arrive in Calgary on time, given that it left Winnipeg on time. Show your work.

40. The probability that a plane will leave Toronto on time is 0.90. The probability that a plane will leave Toronto on time and arrive in Saskatoon on time is 0.53. Determine the probability that a plane will arrive in Saskatoon on time, given that it left Toronto on time. Show your work.

41. Stacey goes to the gym five days a week. Each day, she does a cardio workout using either a treadmill, a stepper, an elliptical walker, or a stationary bike. She follows this with a strength workout using either free weights or the weight machines. Stacey randomly chooses which cardio workout and which strength workout to do each day. Determine the probability that Stacey will use a treadmill and the free weights the next day. Show your work.

42. Lulu goes to the gym five days a week. Each day, she does a cardio workout using either a stepper or an elliptical walker. She follows this with a strength workout using either free weights or the weight machines. Lulu randomly chooses which cardio workout and which strength workout to do each day. Determine the probability that Lulu will use a stepper and the weight machines the next day. Show your work.

43. A paper bag contains a mixture of three types of treats: 12 granola bars, 10 fruit bars, and 8 cheese strips. Suppose that you play a game in which a treat is randomly taken from the bag and replaced, and then a second treat is drawn from the bag. You are allowed to keep the second treat only if it was the same type as the treat that was drawn the first time. Determine the probability that you will be able to keep a granola bar. Show your work.

44. A paper bag contains a mixture of three types of treats: 12 granola bars, 10 fruit bars, and 8 cheese strips. Suppose that you play a game in which a treat is randomly taken from the bag and replaced, and then a second treat is drawn from the bag. You are allowed to keep the second treat only if it was the same type as the treat that was drawn the first time. Determine the probability that you will be able to keep a fruit bar. Show your work.

45. A paper bag contains a mixture of three types of treats: 12 granola bars, 10 fruit bars, and 8 cheese strips. Suppose that you play a game in which a treat is randomly taken from the bag and replaced, and then a second treat is drawn from the bag. You are allowed to keep the second treat only if it was the same type as the treat that was drawn the first time. Determine the probability that you will be able to keep a cheese strip. Show your work.

46.

Anna’s school is holding a chocolate bar sale. For every case of chocolate bars sold, the seller receives a ticket for a prize draw. Anna has sold eight cases, so she has eight tickets for the draw.

At the time of the draw, 130 tickets have been entered. There are two prizes, and the ticket that is drawn for the first prize is returned so it can be drawn for the second prize. Determine the probability that Anna will win both prizes. Show your work.

47.

Anna’s school is holding a chocolate bar sale. For every case of chocolate bars sold, the seller receives a ticket for a prize draw. Anna has sold eight cases, so she has eight tickets for the draw.

At the time of the draw, 130 tickets have been entered. There are two prizes, and the ticket that is drawn for the first prize is returned so it can be drawn for the second prize. Determine the probability that Anna will win no prizes. Show your work.

48. Elin estimates that her probability of passing French is 0.6 and her probability of passing chemistry is 0.8. Determine the probability that Elin will pass both French and chemistry. Show your work.

49. Elin estimates that her probability of passing French is 0.6 and her probability of passing chemistry is 0.8. Determine the probability that Elin will pass French but fail chemistry. Show your work.

50. Elin estimates that her probability of passing French is 0.6 and her probability of passing chemistry is 0.8. Determine the probability that Elin will fail both French and chemistry. Show your work.

40s app prob questions

Answer Section

MULTIPLE CHOICE

1. ANS: B PTS: 1 DIF: Grade 12 REF: Lesson 5.1

OBJ: 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. |

1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.

TOP: Exploring Probability KEY: probability





3. ANS: D PTS: 1 DIF: Grade 12 REF: Lesson 5.1




4. ANS: A PTS: 1 DIF: Grade 12 REF: Lesson 5.1









OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.

TOP: Probability and Odds KEY: probability | odds


OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an

outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.














12. ANS: C PTS: 1 DIF: Grade 12 REF: Lesson 5.2

OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability

or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.















OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or

probability.












OBJ: 5.9 Solve a contextual problem that involves probability and permutations. | 6.4 Solve a contextual problem that involves combinations and probability.

TOP: Probabilities Using Counting Methods KEY: probability | permutation












































OBJ: 2.1 Classify events as mutually exclusive or non-mutually exclusive, and explain the reasoning. | 2.2 Determine if two events are complementary, and explain the reasoning. | 2.3

Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events. | 2.4 Solve a contextual problem that involves the probability of mutually exclusive or non-mutually exclusive events. | 2.5 Solve a contextual problem that involves the probability of complementary events. | 2.6 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.

TOP: Mutually Exclusive Events KEY: probability | mutually exclusive



















Represent, using set notation or graphic organizers, mutually exclusive (including complementary)

and non-mutually exclusive events. | 2.4 Solve a contextual problem that involves the probability of mutually exclusive or non-mutually exclusive events. | 2.5 Solve a contextual problem that involves the probability of complementary events. | 2.6 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.




















Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events. | 2.4 Solve a contextual problem that involves the probability

of mutually exclusive or non-mutually exclusive events. | 2.5 Solve a contextual problem that involves the probability of complementary events. | 2.6 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.









TOP: Mutually Exclusive Events KEY: probability | mutually exclusive | odds










OBJ: 3.2 Determine the probability of an event, given the occurrence of a previous event. | 1.6

Solve a contextual problem that involves odds or probability.

KEY: probability | conditional probability

TOP: Conditional Probability





























KEY: probability | dependent





KEY: probability | dependent





KEY: probability | independent

































OBJ: 3.1 Compare, using examples, dependent and independent events. | 3.3 Determine the probability of two dependent or two independent events. | 3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events. | 1.6 Solve a contextual problem that involves odds or probability.


TOP: Independent Events


OBJ: 3.1 Compare, using examples, dependent and independent events. | 3.3 Determine the probability of two dependent or two independent events. | 3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events. | 1.6 Solve a contextual problem that involves odds or probability. TOP: Independent Events
















OBJ: 3.1 Compare, using examples, dependent and independent events. | 3.3 Determine the

probability of two dependent or two independent events. | 3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events. | 1.6 Solve a contextual problem that involves odds or probability. TOP: Independent Events































SHORT ANSWER

1. ANS:

Yes, the game is fair.

PTS: 1 DIF: Grade 12 REF: Lesson 5.1




2. ANS:

No. Player 1 should score points more often.





3. ANS:

P ( B ) = 0.2





4. ANS:

P ( C ) = 0.2





5. ANS:

P ( C ) = 0.25





6. ANS:




7. ANS:

0.5




8. ANS:

0.4




9. ANS:

1 : 3


OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the

relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.


10. ANS:

3 : 2




11. ANS:

1 : 1




12. ANS:

No. If Josephine had scored 3 times out of 15, then she had not scored 12 times out of 15.

Therefore, the odds in favour are 3 : 12 or 1 : 4.




13. ANS:

No. If Mark had scored 6 times out of 8, then he had not scored 2 times out of 8. Therefore, the odds in favour are 6 : 2 or 3 : 1.




14. ANS:

No. If Ned had scored 5 times out of 25, then he had not scored 20 times out of 25. Therefore, the odds in favour are 5 : 20 or 1 : 4.




15. ANS:

2 : 3




16. ANS:

3 : 2




17. ANS:

3 : 7




18. ANS:

1 : 1




19. ANS:

Yes. The probability of a win is 5 in 8 (62.5%), the probability of a loss is 1 in 4 (25%), and the probability of a tie is 1 in 8 (12.5%). The probabilities add up to 100%.




20. ANS:

Yes. The probability of a win is 7 in 10 (70%), the probability of a loss is 1 in 10 (10%), and the probability of a tie is 1 in 5 (20%). The probabilities add up to 100%.


OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a

probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.


21. ANS:

1.2%




22. ANS:

0.12%




23. ANS:

0.45%




24. ANS:

0.12%




25. ANS:

0.038%




26. ANS:

0.034%




27. ANS:

0.007%




28. ANS:

0.005%




29. ANS:

65%




30. ANS:

37%




31. ANS:

77.5%




32. ANS:

10%




33. ANS:

25%




34. ANS:

60%




35. ANS:

47.6%




36. ANS:

Not mutually exclusive. e.g., 2 is both an even number and a prime number.





37. ANS:

Mutually exclusive. e.g., You cannot roll a sum of 5 and roll a sum of 9 at the same time.





38. ANS:

Not mutually exclusive. e.g. A standard deck of 52 playing cards includes a Jack of hearts.





39. ANS:





40. ANS:





41. ANS:

37.5%





42. ANS:

43.75%





43. ANS:

50%





44. ANS:



Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events. | 2.4 Solve a contextual problem that involves the probability of mutually exclusive or non-mutually exclusive events. | 2.5 Solve a contextual problem that

involves the probability of complementary events. | 2.6 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.


45. ANS:





46. ANS:





47. ANS:

0.7


OBJ: 2.1 Classify events as mutually exclusive or non-mutually exclusive, and explain the

reasoning. | 2.2 Determine if two events are complementary, and explain the reasoning. | 2.3



48. ANS:

0.1





49. ANS:

0.8





50. ANS:

0.6





51. ANS:

These two events are dependent.



Solve a contextual problem that involves odds or probability. TOP: Conditional Probability

KEY: probability | dependent | independent

52. ANS:

These two events are dependent.






53. ANS:

These two events are independent.






54. ANS:

11.1%





55. ANS:

8.3%





56. ANS:

24.5%






57. ANS:

25%






58. ANS:

13.3%





59. ANS:

2.2%






60. ANS:

12.5%






61. ANS:

72.5%






62. ANS:

0.000 657





63. ANS:

0.944






64. ANS:

0.000 202






65. ANS:

0.960





66. ANS:

6.25%




67. ANS:

5%





68. ANS:

4.17%





69. ANS:

9.05%




70. ANS:

6.37%




71. ANS:

15.6%





72. ANS:





73. ANS:




74. ANS:


OBJ: 3.1 Compare, using examples, dependent and independent events. | 3.3 Determine the probability of two dependent or two independent events. | 3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events. | 1.6 Solve

a contextual problem that involves odds or probability.


75. ANS:






76. ANS:

8%




77. ANS:

6%





78. ANS:

Yes. P ( A )



P ( B ) = P ( A



B )





79. ANS:

Yes. P ( A )



P ( B ) = P ( A



B )


OBJ: 3.1 Compare, using examples, dependent and independent events. | 3.3 Determine the probability of two dependent or two independent events. | 3.4 Create and solve a contextual problem that involves determining the probability of dependent or independent events. | 1.6 Solve

a contextual problem that involves odds or probability.



80. ANS:

No. P ( A )



P ( B )



P ( A



B )




PROBLEM

1. ANS:

Jules has 15 attempts and has scored 7 goals. This means that she has 15 – 7 or 8 attempts where she did not score. The odds in favour of her scoring are 7 : 8.

Vicki has 19 attempts and has scored 12 goals. This means that she has 19 – 12 or 7 attempts where she did not score. The odds in favour of her scoring are 12 : 7.

The probability that Jules will score is or about 0.467.

The probability that Vicki will score is or about 0.632.

Since 0.632 > 0.467, there is a better chance that Vicki will score. Therefore, Vicki should go first.




2. ANS:

Leanne has 12 attempts and has scored 8 goals. This means that she has 12 – 8 or 4 attempts where she did not score. The odds in favour of her scoring are 2 : 1.

Krysta has 14 attempts and has scored 9 goals. This means that she has 14 – 9 or 5 attempts where she did not score. The odds in favour of her scoring are 9 : 5.

The probability that Leanne will score is or about 0.667.

The probability that Krysta will score is or about 0.643.

Since 0.667 > 0.643, there is a better chance that Leanne will score. Therefore, Leanne should go first.




3. ANS:

Beth has 9 attempts and has scored 7 goals. This means that she has 9 – 7 or 2 attempts where she did not score. The odds in favour of her scoring are 7 : 2.

Sierra has 13 attempts and has scored 8 goals. This means that she has 13 – 8 or 5 attempts where she did not score. The odds in favour of her scoring are 8 : 5.

The probability that Beth will score is or about 0.778.

The probability that Sierra will score is or about 0.615.

Since 0.778 > 0.615, there is a better chance that Beth will score. Therefore, Beth should go first.




4. ANS:

The odds against winning Zim are 3 : 1. The total number of outcomes is 3 + 1 or 4. So, if she plays Zim 4 times, she is likely to lose 3 times and win 1 time.

The probability of winning Zim is or 0.25.

The odds against winning Bap are 4 : 5. The total number of outcomes is 4 + 5 or 9. So, if she plays Bap 9 times, she is likely to lose 4 times and win 5 times.

The probability of winning Bap is or 0.556.

Sarah should play Bap, since she is more likely to win.


OBJ: 1.1 Provide examples of statements of probability and odds found in fields such as media, biology, sports, medicine, sociology and psychology. | 1.2 Explain, using examples, the relationship between odds (part-part) and probability (part-whole). | 1.3 Express odds as a probability and vice versa. | 1.4 Determine the probability of, or the odds for and against, an outcome in a situation. | 1.5 Explain, using examples, how decisions may be based on probability

or odds and on subjective judgments. | 1.6 Solve a contextual problem that involves odds or probability.


5. ANS:

The odds against winning Zing are 3 : 2. The total number of outcomes is 3 + 2 or 5. So, if she plays Zing 5 times, she is likely to lose 3 times and win 2 times.

The probability of winning Zing is or 0.4.

The odds against winning Bloop are 3 : 7. The total number of outcomes is 3 + 7 or 10. So, if she plays Bloop 10 times, she is likely to lose 3 times and win 7 times.

The probability of winning Bloop is or 0.7.

Lena should play Bloop, since she is more likely to win.




6. ANS:

The odds against winning Boing are 9 : 5. The total number of outcomes is 9 + 5 or 14. So, if she plays Boing 14 times, she is likely to lose 9 times and win 5 times.

The probability of winning Boing is or 0.357.

The odds against winning Zoop are 7 : 2. The total number of outcomes is 7 + 2 or 9. So, if she plays Zoop 9 times, she is likely to lose 7 times and win 2 times.

The probability of winning Zoop is or 0.222.

Sylvia should play Boing, since she is more likely to win.




7. ANS: a) The odds in favour of getting a touchdown are 4 : 6 or 2 : 3.

The odds in favour of getting a field goal, are 7 : 2.

b) The odds in favour of getting 3 points are much better, so the coach should choose the field goal.




8. ANS: a) The odds in favour of getting a touchdown are 8 : 6 or 4 : 3.

The odds in favour of getting a field goal, are 3 : 2. b) Answers may vary. Sample answer: Even though the odds in favour of getting 3 points are slightly better, the team could still lose in overtime. The coach should choose to go for a touchdown.




9. ANS: a) The odds in favour of Denis winning are 55 : (100 – 55). This is equal to 55: 45 or 11 : 9. The odds in favour of Cyndi winning are 25 : (100 – 25). This is equal to 25 : 75 or 1 : 3. The odds in favour of Chris winning are 20 : (100 – 20). This is equal to 20 : 80 or 1 : 4. b) If Chris’ 20% support goes to Cyndi, then her support will now be 45%, and the odds in favour of Cyndi winning will be the same as the odds against Denis winning. So, the odds in favour of

Cyndi winning are 45 : 55 or 9 : 11.




10. ANS:

a) The odds in favour of Jamal winning are 40 : (100 – 40). This is equal to 40: 60 or 2 : 3. The odds in favour of Rebecca winning are 35 : (100 – 35). This is equal to 35 : 65 or 7 : 13. The odds in favour of Henry winning are 25 : (100 – 25). This is equal to 25 : 75 or 1 : 3. b) If Henry’s 25% support goes to Rebecca, then her support will now be 60%, and the odds in favour of Rebecca winning will be the same as the odds against Jamal winning. So, the odds in favour of Rebecca winning are 60 : 40 or 3 : 2.




11. ANS:

Atian, Sam, Phuong, Mike, and Tariq can place first, second, third, fourth, or fifth, in any order.

There are 5! or 120 ways in which five runners can place in five positions.

There are

15

P

5

ways that 15 runners can place first, second, third, fourth, or fifth.

There are 360 360 possible outcomes.

P (A, S, P, M, and T place 1, 2, 3, 4, or 5) =

P (A, S, P, M, and T place 1, 2, 3, 4, or 5) = or

The probability that Atian, Sam, Phuong, Mike, and Tariq will place in the top five positions is

or about 0.03%.




12. ANS:

Greg, Bogdan, Dave, and Li can place first, second, third, or fourth, in any order. There are 4! or

24 ways in which four runners can place in four positions.

There are

12

P

4

ways that 12 runners can place first, second, third, or fourth.

There are 11 880 possible outcomes.

P (G, B, D, and L place 1, 2, 3, or 4) =

P (G, B, D, and L place 1, 2, 3, or 4) = or

The probability that Greg, Bogdan, Dave, and Li will place in the top four positions is or about 0.20%.




13. ANS:

There are 7 letters in total: 2 O’s and 5 other letters.

Let L represent the total number of ways to arrange the letters.

This is the total number of outcomes.

Let R represent the number of ways to spell ONTARIO.

R = 1

You can spell ONTARIO in just 1 way.

So, there is only 1 favourable outcome.

P (winning the car) =


The probability that Gabe will win the car is .




14. ANS:

There are 10 letters in total: 2 O’s, 2 A’s, and 6 other letters.

Let L represent the total number of ways to arrange the letters.

This is the total number of outcomes.

Let R represent the number of ways to spell NOVA SCOTIA.

R = 1

You can spell N0VA SCOTIA in just 1 way.

So, there is only 1 favourable outcome.



The probability that Gabe will win the car is .




15. ANS:

There is an equal likelihood that any of the 20 bikes will be assigned to a participant, since specific bikes cannot be requested.

Let F represent the event that the 5 friends are seated in any row.

The number of ways to seat Jeff and Dariya at either end is 2! or

2

P

2

.

The number of ways to seat the other 3 friends is 3! or

3

P

3

.

The number of ways to seat the other 15 people in the class is 15! or

15

P

15

.

The total number of ways to seat the 5 friends in the first row is (

2

P

2

)(

3

P

3

)(

15

P

15

).

The total number of ways to seat the 5 friends in any row is 4(

2

P

2

)(

3

P

3

)(

15

P

15

).

The total number of ways to assign 20 people to 20 bikes is 20! or

20

P

20

.

The probability that all 5 friends will be in the same row, with Jeff and Dariya at either end, is

.




16. ANS:

There is an equal likelihood that any of the 12 bikes will be assigned to a participant, since specific bikes cannot be requested.

Let F represent the event that the 3 friends are seated in any row.

The number of ways to seat Pia and Amy at either end is 2! or

2

P

2

.

The number of ways to seat the other friend is 1! or

1

P

1

.

The number of ways to seat the other 9 people in the class is 9! or

9

P

9

.

The total number of ways to seat the 3 friends in the first row is (

2

P

2

)(

1

P

1

)(

9

P

9

).

The total number of ways to seat the 3 friends in any row is 4(

2

P

2

)(

1

P

1

)(

9

P

9

).

The total number of ways to assign 12 people to 12 bikes is 12! or

12

P

12

.

The probability that all 3 friends will be in the same row, with Pia and Amy at either end, is .




17. ANS:

Let T represent Tori and Brittany being chosen to play in the infield. Let O represent all possible infield lineups. The number of ways to arrange Tori and Brittany in the infield positions is

4

P

2

. The number of ways to arrange the other 9 players in the remaining 2 infield positions is

9

P

2

.

Therefore, the total number of infield lineups that include Tori and Brittany is (2



3!)

9

P

2

.

The total number of infield lineups possible is

11

P

4

.

The probability can now be determined:

The probability that Tori and Brittany will both play in the infield is . Therefore the odds in favour of this event are 6 : (55 – 6) or 6 : 49.




18. ANS:

Let T represent Tara and Katherine being chosen to play in the outfield. Let O represent all possible outfield lineups. The number of ways to arrange Tara and Katherine in the outfield positions is

3

P

2

. The number of ways to arrange the other 7 players in the remaining outfield

3 position is

7

P

1

. Therefore, the total number of outfield lineups that include Tara and Katherine is

P

2



7

P

1

.

The total number of outfield lineups possible is

9

P

3

.


The probability that Tara and Katherine will both play in the outfield is . Therefore the odds in favour of this event are 1 : (12 – 1) or 1 : 11.




19. ANS:

Let T represent three girls and one boy being chosen to form a subcommittee, and let S represent all possible subcommittees.

In this example, order is not important. The number of ways to arrange three girls and one boy from 12 girls and 8 boys is

12

C

3



8

C

1

.

The number of ways to arrange 20 people in a four-person committee is

20

C

4

.


The odds in favour that the committee will contain 3 girls and 1 boy is 352 : (969 – 352) or 352

: 617.




20. ANS:

Let T represent four girls and three boys being chosen to form a subcommittee, and let S represent all possible subcommittees.

In this example, order is not important. The number of ways to arrange four girls and three boys from 10 girls and 9 boys is

10

C

4



9

C

3

.

The number of ways to arrange 19 people in a seven-person committee is

19

C

7

.


The odds in favour that the committee will contain 4 girls and 3 boys is 1470 : (4199 – 1470) or

1470 : 2729.




21. ANS:

Let A represent the universal set of all model A cars.

Let L represent model A cars with heated leather seats.

Let S represent model A cars with a sunroof.

P ( L



S ) = 100% – 52%

P ( L



S ) = 48%

The probability of a model A car at a dealership having both heated seats and a sunroof is 29%.





22. ANS:

Let A represent the universal set of all model A cars.

Let L represent model A cars with heated leather seats.

Let S represent model A cars with a sunroof.

P ( L



S ) = 100% – 46%

P ( L



S ) = 54%

The probability of a model A car at a dealership having both heated seats and a sunroof is 4%.





23. ANS:

Let D represent the households that have one or more dogs, and let C represent the households that have one or more cats.

P ( D ) = 29%

P ( C ) = 35%

P ( D



C ) = 100% – 42%

P ( D



C ) = 58%

P ( C \ D ) = P ( C ) – P ( D



C )

P ( C \ D ) = 35% – 6%

P ( C \ D ) = 29%

The probability that a household has one or more cats, but no dogs, is 29%.





24. ANS:

Let D represent the households that have one or more dogs, and let C represent the households that have one or more cats.

P ( D ) = 42%

P ( C ) = 28%

P ( D



C ) =100% – 39%

P ( D



C ) = 61%

P ( C \ D ) = P ( C ) – P ( D



C )

P ( C \ D ) = 28% – 9%

P ( C \ D ) = 19%

The probability that a household has one or more cats, but no dogs, is 19%.





25. ANS:

There are 14 stuffed dogs and bears, and 36 other prizes. Therefore, the odds in favour of winning either a stuffed dog or a stuffed bear are 14 : 36, or 7 : 18.





26. ANS:

There are 21 toy cars and books, and 14 other prizes. Therefore, the odds in favour of winning either a toy car or a book are 21 : 14, or 3 : 2.





27. ANS:

There are 18 stuffed lions and yo-yos, and 27 other prizes. Therefore, the odds in favour of winning either a stuffed lion or a yo-yo are 18 : 27, or 2 : 3.





28. ANS:

P ( W ) = 40%

P ( T ) = 50%

P ( W



T ) = 10%

P ( W



T ) = P ( W ) + P ( T ) – P ( W



T )

P ( W



T ) = 40% + 50% – 10%

P ( W



T ) = 80%

The probability that it will snow on Wednesday or on Thursday is 80%.





29. ANS:

Let F represent rain on Friday and let S represent rain on Saturday.

P ( F ) = 40%

P ( S ) = 70%

P ( F



S ) = 20%

P ( F



S ) = P ( F ) + P ( S ) – P ( F



S )

P ( F



S ) = 40% + 70% – 20%

P ( F



S ) = 90%

The probability that it will rain on Friday or on Saturday is 90%.





30. ANS:

Let M represent freezing drizzle on Monday and let T represent freezing drizzle on Tuesday.

P ( M ) = 50%

P ( T ) = 30%

P ( M



T ) = 10%

P ( M



T ) = P ( M ) + P ( T ) – P ( M



T )

P ( M



T ) = 50% + 30% – 10%

P ( M



T ) = 70%

The probability that there will be freezing drizzle on Monday or on Tuesday is 70%.



Represent, using set notation or graphic organizers, mutually exclusive (including complementary) and non-mutually exclusive events. | 2.4 Solve a contextual problem that involves the probability

of mutually exclusive or non-mutually exclusive events. | 2.5 Solve a contextual problem that involves the probability of complementary events. | 2.6 Create and solve a problem that involves mutually exclusive or non-mutually exclusive events.


31. ANS:

Let U = {all natural numbers from 1 to 20}

Let A = {multiples of 3 from 1 to 20}

Let B = {multiples of 2 from 1 to 20}

The universal set has 20 elements, and A



B has 13 elements. Therefore, ( A



B )



must have 20 –

13 or 7 elements. Tristan could have chosen one of 6 numbers. Only three of these numbers are multiples of 3 and 2. Since the probability that Tristan’s number is a multiple of 2 is or ,

P ( B |

A ) = .






32. ANS:

Let U = {all natural numbers from 1 to 35}

Let A = {multiples of 4 from 1 to 35}

Let B = {multiples of 3 from 1 to 35}

The universal set has 35 elements, and A



B has 17 elements. Therefore, ( A



B )



must have 35 –

17 or 18 elements. Reese could have chosen one of 8 numbers. Only two of these numbers are multiples of 4 and 3. Since the probability that Reese’s number is a multiple of 3 is or ,

P ( B |

A ) = .






33. ANS:

P (windy) is 30%, so P (calm) is 100% – 30% or 70%.

P (win | windy) = 50%

P (lose | windy) = 100% – 50% or 50%

P (win | calm) = 70%

P (lose | calm) = 100% – 70% or 30%

P (win) = P (windy



win) + P (calm



win)

P (win) = 0.15 + 0.49

P (win) = 0.64

The probability that Debra’s team will win tomorrow is 64%.






34. ANS:

P (windy) is 60%, so P (calm) is 100% – 60% or 40%.

P (win | windy) = 60%

P (lose | windy) = 100% – 60% or 40%

P (win | calm) = 80%

P (lose | calm) = 100% – 80% or 20%

P (win) = P (windy



win) + P (calm



win)

P (win) = 0.36 + 0.32

P (win) = 0.68

The probability that Rowan’s team will win tomorrow is 68%.






35. ANS:

Let T represent a true or false question, and let M represent a multiple-choice question. Let C represent a correct question.

P ( T



C ) = P ( T )



P ( C | T )

P ( T



C ) = 0.2



0.7

P ( T



C ) = 0.14

P ( M



C ) = P ( M )



P ( C | M )

P ( M



C ) = 0.8



0.9

P ( M



C ) = 0.72

P ( C ) = 0.14 + 0.72

P ( C ) = 0.86

The probability the question was multiple-choice is , or about 0.837 or 83.7%.






36. ANS:

Let T represent a true or false question, and let M represent a multiple-choice question. Let C represent a correct question.

P ( T



C ) = P ( T )



P ( C | T )

P ( T



C ) = 0.4



0.7

P ( T



C ) = 0.28

P ( M



C ) = P ( M )



P ( C | M )

P ( M



C ) = 0.6



0.8

P ( M



C ) = 0.48

P ( C ) = 0.28 + 0.48

P ( C ) = 0.76

The probability the question was multiple-choice is , or about 0.632 or 63.2%.






37. ANS:

Let S represent Mena remembering to set her alarm, and let N represent Mena not remembering to set her alarm. Let L represent Mena being late for school.

P ( S



L ) = P ( S )



P ( L | S )

P ( S



L ) = 0.71



0.10

P ( S



L ) = 0.071

P ( N



L ) = P ( N )



P ( L | N )

P ( N



L ) = 0.29



0.80

P ( N



L ) = 0.232

P ( C ) = 0.071 + 0.232

P ( C ) = 0.303

The probability Mena’s alarm clock was set is

, or about 0.234 or 23.4%.






38. ANS:

Let S represent Trista remembering to set her alarm, and let N represent Trista not remembering to set her alarm. Let L represent Trista being late for school.

P ( S



L ) = P ( S )



P ( L | S )

P ( S



L ) = 0.82



0.30

P ( S



L ) = 0.246

P ( N



L ) = P ( N )



P ( L | N )

P ( N



L ) = 0.18



0.60

P ( N



L ) = 0.108

P ( C ) = 0.246 + 0.108

P ( C ) = 0.354

The probability Trista’s alarm clock was set is

, or about 0.695 or 69.5%.






39. ANS:

Let L represent a plane leaving from Winnipeg on time, and let A represent a plane arriving in

Calgary on time.

P ( L ) = 0.80

P ( L



A ) = 0.42

The probability that a plane will arrive in Calgary on time, given it left Winnipeg on time, is 0.525 or 52.5%.






40. ANS:

Let L represent a plane leaving from Toronto on time, and let A represent a plane arriving in

Saskatoon on time.

P ( L ) = 0.90

P ( L



A ) = 0.53

The probability that a plane will arrive in Saskatoon on time, given it left Toronto on time, is about

0.589 or 58.9%.






41. ANS:

Let T represent Stacey using a treadmill.

Let F represent Stacey using free weights.

P ( T ) =

P ( F ) =

P ( T



F ) = P ( T )



P ( F )

P ( T



F ) =

P ( T



F ) =

The probability Stacey will use a treadmill and the free weights for her next workout is , or 0.125 or 12.5%.





42. ANS:

Let S represent Lulu using a stepper.

Let M represent Lulu using weight machines.

P ( S ) =

P ( M ) =

P ( S



M ) = P ( S )



P ( M )

P ( S



M ) =

P ( S



M ) =

The probability Lulu will use a stepper and the weight machines for her next workout is , or 0.25 or 25%.




43. ANS:

Let G represent drawing a granola bar.

P ( G ) =

P ( G ) =

P ( G



G ) =

P ( G



G ) =

The probability that a granola bar is kept is , or 0.16 or 16%.





44. ANS:

Let F represent drawing a fruit bar.

P ( F ) =

P ( F ) =

P ( F



F ) =

P ( F



F ) =

The probability that a fruit bar is kept is , or about 0.111 or 11.1%.




45. ANS:

Let S represent drawing a cheese strip.

P ( S ) =

P ( S ) =

P ( S



S ) =

P ( S



S ) =

The probability that a cheese strip is kept is , or about 0.071 or 7.1%.





46. ANS:

Let W represent Anna winning the first prize, and let X represent winning the second prize.

P ( W ) =

P ( W ) =

P ( X ) =

P ( W



X ) = P ( W )



P ( X )

P ( W



X ) =

P ( W



X ) =

The probability that Anna wins both prizes is , or about 0.0038 or 0.38%.




47. ANS:

Let W represent Anna winning the first prize, and let X represent winning the second prize.

P ( W



) = 1 – P ( W )

P ( W



) = 1 –

P ( W



) =

P ( W



) =

P ( W



) = P ( X



)

P ( W

 

X



) = P ( W



)



P ( X



)

P ( W

 

X



) =

P ( W

 

X



) =

The probability that Anna wins neither prize is , or about 0.8807 or 88.07%.




48. ANS:

Let F represent passing French, and let C represent passing chemistry.

P ( F ) = 0.6

P ( C ) = 0.8

P ( F



C ) = P ( F )



P ( C )

P ( F



C ) = 0.6



0.8

P ( F



C ) = 0.48

The probability that Elin will pass both French and Chemistry is 0.48, or 48%.





49. ANS:


P ( F ) = 0.6

P ( C



) = 0.2

P ( F



C



) = P ( F )



P ( C



)

P ( F



C



) = 0.6



0.2

P ( F



C



) = 0.12

The probability that Elin will pass French but fail Chemistry is 0.12, or 12%.




50. ANS:


P ( F



) = 0.4

P ( C



) = 0.2

P ( F

 

C



) = P ( F )



P ( C



)

P ( F

 

C



) = 0.4



0.2

P ( F

 

C



) = 0.08

The probability that Elin will fail both French and chemistry is 0.08, or 8%.




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