Name: _______________________
Period: ____
Chapter 4 Review: Must Show All Work!
Mutually Exclusive Events:
I. Determine whether these events are mutually exclusive.
1) Roll a die: get an even number and get a number greater than 4
2) Roll a die: get an even number and get an odd number.
3) Pick a card from a deck: get a heart and get a jack
Addition Rule: Probability of A or B Occuring:
4) An automobile dealer decides to select a month for its annual sale. Find the probability
that it will be December or January.
5) In a statistics class there are 20 juniors and 9 seniors; 5 of the seniors are females and 8
of the juniors are males. If a student is selected at random, find the probability of
selecting the following:
a) P(a junior or a female)
b) P(a senior or a female)
c) P(a junior or a senior)
6) At a particular school with 250 male students, 48 play football, 35 play basketball and
12 play both. Find the probability that a randomly selected male student plays basketball
or football. Find the probability that a randomly selected male student plays neither
sport.
7) The probability that s student owns a car is 0.45, and the probability that a student
owns a computer is 0.85. If the probability that a student owns both is 0.35, what is the
probability that a randomly selected student owns a car or computer? What is the
probability that a randomly selected student does not own a car or computer?
Multiplication Rule:
8) If 2 cards are selected from a standard deck of cards. The first card is placed back in
the deck before the second card is drawn. Find the following probabilities:
a) P(Heart and club)
b) P( Red card and Spades face card)
c) P(Queen of hearts and King)
d) P(Spade and 3 of hearts)
9) Find the same probabilities for problem #8 but this time, the card is not placed back in
the deck before the 2nd card is drawn.
10) A flashlight has 6 batteries, 2 of which are defective. If 2 are selected at random
without replacement, find the probability that both are defective.
Conditional Probability:
11) The medal distribution from 2000 Summer Olympic Games is shown on the table.
COUNTRY
GOLD
SILVER
BRONZE
United States
39
25
33
Russia
32
28
28
China
28
16
15
Australia
16
25
17
Find these probabilities:
a) Find the probability that the winner won the gold medal, given that the winner was
from Russia.
b) Find the probability that the winner was from the US, given that she or he won a silver
medal.
12)
The probability that Janice smokes is 2/9. The probability that she
Smokes and develops lung cancer is 1/11. Find the probability that
Janice develops lung cancer, given that she smokes.
13)
A penny and a nickel are tossed. Find the probability that the penny
Shows heads, given that the nickel shows heads.
14) A box contains three blue marbles, five red marbles, and four white
marbles. If one marble is drawn at random, find:
a) P(blue | not white)
b) P(not red | not white)
Permutations:
15) In how many different ways can 7 floats line up for the homecoming parade.
16) In how many ways can 4 of 7 different kinds of bushes be planted along a walkway?
17) Four processes are involved in assembling a certain product and they can be
performed in any order. The management wants to test each order to determine which is
the least time consuming. How many different orders will have to be tested?
18) A roofing company has 8 roofing jobs to complete in the next 2 months.
a) In how many different orders can the roofing jobs be completed?
b) If 5 of the 8 roofing jobs can be completed by the end of the first month, in how
many different ways can the first 5 jobs be selected?
III. Combinations:
19) Your friend is having a party and has 15 games to choose from. There is enough
time to play 4 games. In how many ways can you choose 4 games to play?
20) There are 20 members in a club. Five people are selected to go to the state
conference. In how many ways can the five members be selected?
21) Your English teacher asked you to read 3 novels from a list of 10. In how many
ways can you choose which books to read?
22) The general manager of a fast-food restaurant chain must select 6 restaurants from
11
for a promotional program. How many possible ways can this selection be done?
Probability and Odds:
23) Sammy has a number cube (dice). Calculate the following:
What is the probability of rolling a 4?
What is the probability of not rolling a 4?
What are the odds in favor of rolling a 4?
What are the odds against rolling a 4?
What are the odds in favor of rolling an even number?
What are the odds against rolling an even number?
Pay-off Odds
24. When Juno won the Kentucky Derby, a 4 dollar bet that Juno would win would result in
a return of 31 dollars.
a. How much net profit was made from a 4 dollar win bet on Juno?
b. What were the payoff odds against a Juno win?
c. Based on a preliminary wagering before the race, betters collectively believed that
Juno had a 4/29 probability of winning. Assuming that 4/29 was the true probability
of a Juno victory, what were the actual odds against his winning?
d. If the payoff odds were the actual odds found in part c, how much would a 4 dollar
ticket be worth after a Juno win?
ANSWER KEY BELOW
Mutually Exclusive Events:
I. Determine whether these events are mutually exclusive.
1) Roll a die: get an even number and get a number greater than 4
Answer: no
2) Roll a die: get an even number and get an odd number.
Answer: yes
3) Pick a card from a deck: get a heart and get a jack
Answer: no
Addition Rule: Probability of A or B Occuring:
4) An automobile dealer decides to select a month for its annual sale. Find the probability
that it will be December or January.
Answer: 1/12 +1/12 = 1/6
5) In a statistics class there are 20 juniors and 9 seniors; 5 of the seniors are females and 8
of the juniors are males. If a student is selected at random, find the probability of
selecting the following:
a) P(a junior or a female) Answer: 20/29 + 17/29 - 12/29 = 25/29 =.862
b) P(a senior or a female)Answer: 9/29 + 17/29 - 5/29 = 21/29 = .724
c) P(a junior or a senior)Answer: 20/29 + 9/29 = 29/29 = 1
6) At a particular school with 250 male students, 48 play football, 35 play basketball and
12 play both. Find the probability that a randomly selected male student plays basketball
or football. Find the probability that a randomly selected male student plays neither
sport.
Answer: 48/250 +35/250 -12/250 = 71/250 = .284
Answer: 1-.284 = .716
7) The probability that s student owns a car is 0.45, and the probability that a student
owns a computer is 0.85. If the probability that a student owns both is 0.35, what is the
probability that a randomly selected student owns a car or computer? What is the
probability that a randomly selected student does not own a car or computer?
Answer: .45 + .85 - .35= .95
Answer: 1-.95= .05
Multiplication Rule:
8) If 2 cards are selected from a standard deck of cards. The first card is placed back in
the deck before the second card is drawn. Find the following probabilities:
a) P(Heart and club) Answer: 13/52 * 13/52 = 169/2704= 1/16 or .0625
b) P( Red card and Spades face card) Answer: 26/52 * 3/52= .0288
c) P(Queen of hearts and King) Answer: 1/52 * 4/52 = .00148
d) P(Spade and 3 of hearts) Answer: 13/52 * 1/52= .00481
9) Find the same probabilities for problem #8 but this time, the card is not placed back in
the deck before the 2nd card is drawn. Answer: a) 13/52 *13/51= .0637
Answer: b) 26/52 * 3/51= .0294
Answer: c) 1/52 * 4/51= .00151
Answer: d) 13/52 * 1/51= .004902
10) A flashlight has 6 batteries, 2 of which are defective. If 2 are selected at random
without replacement, find the probability that both are defective.
Answer: 2/6 * 1/5 = 2/30= 1/15= .0667
Conditional Probability:
11) The medal distribution from 2000 Summer Olympic Games is shown on the table.
COUNTRY
GOLD
SILVER
BRONZE
United States
39
25
33
Russia
32
28
28
China
28
16
15
Australia
16
25
17
Find these probabilities:
a) Find the probability that the winner won the gold medal, given that the winner was
from Russia. Answer: 32/88= .364
b) Find the probability that the winner was from the US, given that she or he won a silver
medal. Answer: 25/94= .266
12)
The probability that Janice smokes is 2/9. The probability that she
Smokes and develops lung cancer is 1/11. Find the probability that
Janice develops lung cancer, given that she smokes.
Answer: (1/11) / (2/9) = .409
13)
A penny and a nickel are tossed. Find the probability that the penny
Shows heads, given that the nickel shows heads.
Answer: P(A|B) = P(A and B) / P(B); P(Penny shows heads|Nickel shows heads)= P
(both) divided by P(Nickel showing heads). (½ * ½ ) / (½ )= (¼) /( ½ )= ½
14) A box contains three blue marbles, five red marbles, and four white
marbles. If one marble is drawn at random, find:
a) P(blue | not white) Answer: 3/8
b) P(not red | not white) Answer: 3/8
Permutations:
15) In how many different ways can 7 floats line up for the homecoming parade.
Answer: 7!= 5,040
16) In how many ways can 4 of 7 different kinds of bushes be planted along a walkway?
Answer: 7 * 6 * 5 * 4 = 840
17) Four processes are involved in assembling a certain product and they can be
performed in any order. The management wants to test each order to determine which is
the least time consuming. How many different orders will have to be tested?
Answer: 4!= 24
18) A roofing company has 8 roofing jobs to complete in the next 2 months.
a) In how many different orders can the roofing jobs be completed?
Answer: 8!= 40, 320
b) If 5 of the 8 roofing jobs can be completed by the end of the first month, in how
many different ways can the first 5 jobs be selected?
Answer: 8 * 7 * 6 * 5 * 4 = 6720
III. Combinations:
19) Your friend is having a party and has 15 games to choose from. There is enough
time to play 4 games. In how many ways can you choose 4 games to play?
Answer: (15 * 14 * 13 * 12) / (4 * 3 * 2 * 1) = 1,365
20) There are 20 members in a club. Five people are selected to go to the state
conference. In how many ways can the five members be selected?
Answer: (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1) = 15,504
21) Your English teacher asked you to read 3 novels from a list of 10. In how many
ways can you choose which books to read?
Answer: (10 * 9 * 8)/ (3 * 2 * 1) = 120
22) The general manager of a fast-food restaurant chain must select 6 restaurants from
11
for a promotional program. How many possible ways can this selection be done?
Answer: (11 * 10 * 9 * 8 * 7 * 6) / (6 * 5 * 4 * 3 * 2 * 1)= 332640/720=462
Probability and Odds:
23) Sammy has a number cube (dice). Calculate the following:
What is the probability of rolling a 4? Answer: 1/6
What is the probability of not rolling a 4? Answer: 5/6
What are the odds in favor of rolling a 4? Answer: 1:5
What are the odds against rolling a 4? Answer: 5:1
What are the odds in favor of rolling an even number? Answer: 1:1
What are the odds against rolling an even number? Answer: 1:1
Pay-off Odds
25. When Juno won the Kentucky Derby, a 4 dollar bet that Juno would win would result in
a return of 31 dollars.
a. How much net profit was made from a 4 dollar win bet on Juno? Answer: 27$
b. What were the payoff odds against a Juno win? Answer: 27:4
c. Based on a preliminary wagering before the race, betters collectively believed that Juno
had a 4/29 probability of winning. Assuming that 4/29 was the true probability of a Juno
victory, what were the actual odds against his winning? Answer: 25:4
d. If the payoff odds were the actual odds found in part c, how much would a 4 dollar
ticket be worth after a Juno win? Answer: Payoff odds: 25:4, therefore a 4 dollar ticket
yields a profit of 25$; however, when turning the ticket in you get 29$, because you
are receiving 25$ in profit AND your original 4 dollars you spent on the bet. So the
ticket when handed in would be worth 29$.