STUDY GUIDE- TEST 1
1. 84 chips numbered from 1 to 84 are placed in a barrel. One chip is randomly
pulled from the barrel. What is the probability that the number on the chip is
greater than or equal to 38?
2. Mickey is buying a new car. He has to pick 1 color for the interior and 1 color for
the exterior. This particular car has 4 options for the interior color and 8 options
for the exterior color. How many possible combinations does Mickey have from
which to choose?
3. In the lake there are 3 times as many largemouth bass as there are smallmouth
bass. If Johnny randomly catches a bass at the lake, what is the probability that
Johnny caught a smallmouth bass?
4. Brian wants to buy a new bicycle. Bicycles Galore has 5 different bicycles that
Brian is interested in. Cycles Unlimited has 11 different bicycles that Brian is
interested in. How many possible choices does Brian have for his new bicycle?
5. An experiment consists of rolling a fair die three times. What is the probability of
getting a number divisible by 3 on all three rolls?
6. Callie's gym has 3 different leg press machines and 10 different cardio machines.
If Callie wants to use 1 leg press machine and 1 cardio machine, how many
possible combinations does she have?
7. Laura has a shiny new quarter. If she flips this coin twice, what is the probability
that she will get heads both times?
8. Brent owns 8 suits and 12 ties. He wants to pick out a suit and tie to wear to his
cousin's wedding. How many possible combinations does he have?
9.
An experiment consists of rolling two fair dice and adding the dots on the two
sides facing up. What is the probability that the sum of the dots is divisible by 4?
10. Dippin' Donuts has 15 different flavors of donuts and 7 different flavors of coffee.
Jessie wants 1 donut and 1 cup of coffee. How many possible combinations does
Jessie have from which to choose?
11. Elizabeth works in quality control for a clothing company. At her company, the
probability of no items being defective in a shipment is 1/7, and the probability of
a shipment having only one defective item is 2/7. What is the probability that a
shipment of items from Elizabeth's company has less than two defective items?
12. Sandra has 4 different jackets and 11 scarves. On a cold day, she wants to wear
1 jacket and 1 scarf. How many possible combinations could she choose to wear?
13.
An experiment consists of rolling two fair dice and adding the dots on the two
sides facing up. What is the probability that the sum of the dots is 7 or 11?
14. Sally is deciding where to eat lunch. There are 18 take-out restaurants and 11
dine-in restaurants near her job. If she can only choose 1 restaurant for lunch
today, how many possible choices does she have?
15. A restaurant serves lemonade, tea, water, coffee, lemon-lime soft drink, and cola
soft drink. Brighton ordered lemon-lime soft drink, and his mother ordered tea. If
their waitress forgot their order and had to guess which drinks to bring them,
what is the probability that she will get their order right?
16. Alana is supposed to pick out 1 fruit and 1 vegetable to eat with her dinner. She
has 7 fruits and 5 vegetables from which to choose. How many possible
combinations does she have?
17. A spinner was spun 40 times. The results are shown in the table below.
Spinner
Results
Yellow
11
White
8
Red
6
Blue
6
Green
4
Orange
5
Which color's experimental probability matches its theoretical probability?
18. An experiment consists of first flipping a fair coin. If the coin lands on heads,
then a fair die is rolled. If the coin lands on tails, then the coin is flipped again.
How many possible outcomes have at least one tail?
19.
An experiment consists of rolling two fair dice and adding the dots on the two
sides facing up. What is the probability that the sum of the dots is 3?
20. Alex can pick 1 type of cereal for breakfast and 1 type of sandwich for lunch. He
has 8 choices for a cereal and 4 choices for a sandwich. How many possible
combinations does Alex have?
21. The Juniors and Seniors at Pollyville High School are hosting a golf tournament to
raise money for the prom. A total of 18 teams of four signed up for the
tournament. A random drawing is being held to determine the tee off order. If
the Junior class signed up 10 foursomes for the tournament, what is the
probability that the foursome drawn first was signed up by the Senior class?
22. Vera could order either a soup or salad appetizer to go with her dinner. The
menu had 4 different salads and 2 different soups from which to choose. How
many possible appetizers could Vera order?
23. A six sided die is rolled. What is the probability that either a 5 or 6 is rolled?
24. An experiment consists of first flipping a fair coin. If the coin lands on heads,
then a fair die is rolled. If the coin lands on tails, then the coin is flipped again.
How many possible outcomes have an odd number ?
25. A spinner has 9 equal-sized spaces. It has 2 red spaces, 3 green spaces, 2 yellow
spaces, and 2 orange spaces. If Jake spins the spinner 2 times, what is the
probability he will get an orange space on the first spin and a green space on the
second spin?
26. Drake has time to do one chore and play one video game. He has 4 chores he
could choose to do, and he has 10 video games from which to choose. How many
possible combinations does Drake have?
27. Carla has 17 stickers of different colors. She figures that if she chooses a sticker
without looking, her probability of getting a purple sticker is 12/17. What is the
probability of getting a sticker other than a purple sticker?
28. An experiment consists of flipping a fair coin and rolling a fair die. How many
possible outcomes have an odd number ?
29. Teresa has a copy of her school directory on her desk. Students whose last
names start with the letters A-F occupy the first 4 pages of the book. Those
students with last names G-M occupy the next 7 pages, those with last names NR the following 7 pages, and those with last names S-Z the final 10 pages. If she
opens up the directory and picks out a student at random, what is the probability
that this student’s last name begins with a letter from the first half of the
alphabet?
30. An experiment consists of drawing two balls out of an urn with replacement. The
urn has 1 red ball, 1 white ball, and 1 blue ball. How many possible outcomes are
there?
31. The following chips are placed in a bucket: 2 red, 5 yellow, 5 blue, and 6 green.
One chip is randomly selected from the bucket. What is the probability that the
chip is either yellow or green?
32. An experiment consists of flipping a fair coin and rolling a fair die. How many
possible outcomes have a tail and a number divisible by 2?
33. Braiden has gone on a field trip with his class to the zoo. However, he has gotten
lost. It is now time to leave, and he needs to find the right bus to get on to go
back to school. Braiden attends Cheyenne Middle School. In the parking lot,
there are 4 buses from Cheyenne Middle School, 3 buses from Farmington
Elementary, and 6 buses from Hollis Middle School. Unfortunately, all these
buses look alike. If Braiden goes up to a bus at random, what is the probability
that it will be the wrong bus?
34. Trout Pro Shop sells 13 different fishing rods and 6 different tackle boxes. If Sam
wants to buy 1 fishing rod and 1 tackle box, how many possible combinations
does he have?
35. Grace is planting a garden in her backyard. She has 3 packets of tomato seeds, 5
packets of corn seeds, and 7 packets of cucumber seeds. Each packet has
enough seeds to plant one row of vegetables. What is the probability that Grace
plants a row of cucumbers, then a row of corn?
36. Smithville School District, which has two high schools, is giving away a new car
to one lucky high school senior. East Smithville High has 599 seniors in the
lottery, and West Smithville High has 847 seniors in the lottery. How many
possible winners are there for the new car?
37. An experiment consists of rolling a fair die and flipping a fair coin. What is the
probability of getting a number divisible by 3 and a head?
38. Jim & Larry's Ice Cream Shoppe sells 18 different flavors of ice cream. They also
have 6 different ice cream toppings. If Jan wants to buy an ice cream cone with
exactly 1 flavor of ice cream and 1 topping, how many possible combinations
does she have from which to choose?
39. Javier and Jackson bought tickets to a raffle. Javier bought 4 tickets, Jackson
bought 7 tickets, and 74 total tickets were sold. What is the probability that
either Javier or Jackson will win the raffle?
40. Nick has 14 baseball hats and 11 cowboy hats. If he wants to wear 1 hat today,
how many possible choices does he have?
Answers
1.
/84
47
2. 32
3.
/4
1
4. 16
5.
/27
1
6. 30
7.
/4
1
8. 96
9.
/4
1
10. 105
11. 3/7
12. 44
13. 2/9
14. 29
15. 1/36
16. 35
17. Orange
18. 2
19. 1/18
20. 32
21. 0.44
22. 6
23. 1/3
24. 3
25. 2/27
26. 40
27. 5/17
28. 6
29.
/28
11
30. 9
31.
/18
11
32. 3
33. 9/13
34. 78
35. 1/6
36. 1,446
37. 1/6
38. 108
39.
/74
11
40. 25
Explanations
1. There are 84 chips in a barrel. Of those 84 chips, 47 of them have the number 38 or greater on
them.
Therefore, the probability that the number on the chip is greater than or equal to 38 is
47
/84.
2. For every interior color, there are 8 different exterior colors that Mickey could pick. So, for each
interior color, there are 8 possible combinations. Since there are 4 interior colors, multiply 8
possible combinations per interior color times 4 interior colors to get the total number of possible
combinations.
4 × 8 = 32 possible combinations
3. Remember there are 3 times as many largemouth bass as there are smallmouth bass.
So, for example, if there were 3 smallmouth bass in the lake, then there would be 9 largemouth
bass in the lake.
Out of 12 bass in the lake, 3 are smallmouth bass. So, the probability of catching a smallmouth
bass is 3/12, which reduces to 1/4.
4. Brian will only buy 1 bicycle. There are 5 possible bicycles at Bicycles Galore or 11 possible bicycles
at Cycles Unlimited. The total number of possible bicycles he could buy is 5 + 11 = 16 bicycles. So,
Brian has 16 possible choices.
5. Each roll of the die is independent of the previous roll. So, the probability of getting a number
divisible by 3 on all three rolls is the product of the probabilities of getting a number divisible by 3
on each roll.
The probability of getting a number divisible by 3 on a single roll is 1/3. So, the probability of
getting a number divisible by 3 on all three rolls is
(1/3)(1/3)(1/3) = 1/27
6. For every leg press machine, there are 10 different cardio machines that Callie could use. So, for
each leg press machine, there are 10 possible combinations. Since there are 3 leg press machines,
multiply 10 possible combinations per leg press machine times 3 leg press machines to get the
total number of possible combinations.
3 × 10 = 30 possible combinations
7. If Laura flips her quarter twice, there are 4 possible outcomes, each with equal probability ("H"
stands for "heads" and "T" for "tails"):
{H, H}, {H, T}, {T, H}, and {T, T}
The only outcome that corresponds to getting heads both times is {H, H}. So, the probability that
Laura gets heads both times is 1/4.
8. For every suit, there are 12 different choices of a tie that Brent could wear. So, for each suit, there
are 12 possible combinations. Since there are 8 suits, multiply 12 possible combinations per suit
times 8 suits to get the total number of possible combinations.
8 × 12 = 96 possible combinations
9. 4, 8, and 12 are all divisible by 4.
There are 3 combinations that sum to 4, 5 combinations that sum to 8, and 1 combination that
sums to 12. This gives a total of 9 combinations out of a possible 36 that are divisible by 4.
So, the probability that the sum is divisible by 4 is 9/36 = 1/4.
10. For every donut flavor, there are 7 different coffee flavors that Jessie could choose. So, for each
donut, there are 7 possible combinations. Since there are 15 donuts, multiply 7 possible
combinations per donut times 15 donuts to get the total number of possible combinations.
15 × 7 = 105 possible combinations
11. If a shipment has less than two defective items, it can either have one defective item or zero
defective items.
To find the probability that a shipment has less than two defective items, add the probability that
the shipment has one defective item and the probability that the shipment has zero defective
items.
/7 + 1/7 = 3/7
2
12. For every jacket, there are 11 different scarves that Sandra could wear. So, for each jacket, there
are 11 possible combinations. Since there are 4 jackets, multiply 11 possible combinations per
jacket times 4 jackets to get the total number of possible combinations.
4 × 11 = 44 possible combinations
13. There are 6 combinations out of a possible 36 that sum to 7 and 2 combinations out of a possible
36 that sum to 11. Combined, there are a total of 8 combinations out of 36 that sum to 7 or 11.
So, the probability that the sum of the dots is 7 or 11 is 8/36 = 2/9.
14. Sally gets to choose only 1 restaurant. There are 18 possible take-out restaurants she could order
from or 11 dine-in restaurants she could eat at. The total number of possible restaurants she could
choose is 18 + 11 = 29 restaurants. So, Sally has 29 possible choices.
15. There are six types of drinks total. Brighton chose 1 drink, lemon-lime soda, so the probability the
waitress guesses his drink correctly is 1/6.
Brighton's mother chose 1 drink, tea, so the probability the waitress guesses her drink correctly is
1
/6.
Multiply the probabilities to find the probability that the waitress guesses both their drinks
correctly.
/6 × 1/6 = 1/36
1
16. For every fruit, there are 5 different choices of a vegetable that Alana could eat. So, for each fruit,
there are 5 possible combinations. Since there are 7 fruits, multiply 5 possible combinations per
fruit times 7 fruits to get the total number of possible combinations.
7 × 5 = 35 possible combinations
17. Since the Yellow and White sections each cover 1/4 of the spinner, theoretically the spinner should
land on each of these colors 1/4 of the time or 10 times.
Since the Red, Blue, Green, and Orange sections cover 1/8 of the spinner, theoretically the spinner
should land on each of these colors 1/8 of the time or 5 times.
So, Orange is the only color whose experimental probability matched its theoretical probability.
18. Looking at the tree diagram we see that there are 8 possible outcomes. If the first flip of the coin
is a head, then none of the outcomes from rolling the die has at least one tail. If the first flip of the
coin is a tail, then there are two outcomes with at least one tail. So, of the possible 8 outcomes, 0
+ 2 or 2 have at least one tail.
19. There are 2 combinations that sum to 3 out of the 36 possible outcomes.
So, the probability that the sum of the dots is 3 is 2/36 = 1/18.
20. For every cereal, there are 4 different sandwiches that Alex could choose. So, for each cereal,
there are 4 possible combinations. Since there are 8 cereals, multiply 4 possible combinations per
cereal times 8 cereals to get the total number of possible combinations.
8 × 4 = 32 possible combinations
21. There are 18 teams of four. If 10 of them were signed up by the Junior class, then 8 of them were
signed up by the Senior class.
So, the probability that the foursome drawn first was signed up by the Senior class is 8/18, or 0.44.
22. Vera gets to choose only 1 appetizer. There are 4 possible salads she could order or 2 possible
soups she could order. The menu of possible appetizers she could order is 4 + 2 = 6 appetizers.
So, Vera has 6 possible choices.
23. The probability of rolling a 5 is 1/6.
The probability of rolling a 6 is 1/6.
/6 + 1/6 = 2/6 = 1/3
1
.
24. Looking at the tree diagram we see that there are 8 possible outcomes. By restricting the
outcomes to those that have a head on the first flip of the coin we cut the number of outcomes
down to 6. Of the 6 remaining outcomes, 3 are odd. So, 3 of the 8 possible outcomes have an odd
number.
25. The question asks for the prediction of two events that follow each other. The probability of getting
an orange space is 2/9, and the probability of getting the green space is 1/3.
To find the probability of getting them in that order, multiply the 2 probabilities together.
/9 × 1/3 = 2/27
2
26. For every chore, there are 10 different choices of a video game that Drake could play. So, for each
chore, there are 10 possible combinations. Since there are 4 chores, multiply 10 possible
combinations per chore times 4 chores to get the total number of possible combinations.
4 × 10 = 40 possible combinations
27. Twelve of the 17 stickers are purple, then the probability of getting a purple sticker is
draws 1 time.
/17. Carla
12
If P is the probability of an event, 1-P is the probability of an event not occurring.
So in this case, the probability of picking a sticker that is not purple is 1 -
/17 = 5/17.
12
28. Looking at the tree diagram we see that there are 12 possible outcomes. Since the problem is only
concerned with the number on the die and not the coin, we need to look at all 12 outcomes. 6 are
odd. So, 6 of the 12 possible outcomes have an odd number.
29. The directory contains 28 pages in all. Since we want to find the probability that Teresa picks a
student whose last name begins with a letter from the first half of the alphabet, we first need to
determine the range of the letters from the first half of the alphabet. There are 26 letters in the
alphabet, and the first 13 are A-M. Students whose last names start with A-M occupy the first 4 +
7 = 11 pages of the directory. So, the probability that Teresa picks a student whose last name
starts with A-M is 11/28.
30. Looking at the tree diagram we see that there are 9 possible outcomes. .
31. There are 18 chips in the bucket altogether.
5 of them are yellow.
6 of them are green.
So, 11 chips are either yellow or green.
Therefore, the probability that the selected chip is either yellow or green is 11 out of 18, or
11
/18.
32. Looking at the tree diagram we see that there are 12 possible outcomes. By restricting the
outcomes to those that have a tail we cut the number of outcomes down to 6. Of the 6 remaining
outcomes, 3 are divisible by 2. So, 3 of the 12 possible outcomes have a tail and a number
divisible by 2.
33. Braiden attends Cheyenne Middle School. Since Braiden is lost and needs to get back to school, he
wants to get on a bus from Cheyenne Middle School. The buses from Farmington Elementary and
Hollis Middle School are the wrong buses. There are 13 buses in the parking lot. Farmington
Elementary has 3 buses and Hollis Middle School has 6 buses, so there are 3 + 6 = 9 wrong
buses. So, the probability that he picks a wrong bus is 9/13.
34. For every fishing rod, there are 6 different tackle boxes that Sam could buy. So, for each fishing
rod, there are 6 possible combinations. Since there are 13 fishing rods, multiply 6 possible
combinations per fishing rod times 13 fishing rods to get the total number of possible
combinations.
13 × 6 = 78 possible combinations
35. Grace has 7 packets of cucumber seeds and 15 total packets of seeds. So, the probability of Grace
planting a row of cucumbers is 7/15.
After Grace uses one packet of cucumber seeds, she has 5 packets of corn seeds and 14 total
packets of seeds. So, the probability that Grace plants a row of corn after the row of cucumbers is
5
/14.
Multiply the probabilities to find the probability that Grace plants a row of cucumbers, then a row
of corn.
/15 × 5/14 = 1/6
7
36. Only 1 senior will win the car. There are 599 possible winners from East Smithville High and 847
possible winners from West Smithville High. The total number of possible winners is 599 + 847 =
1,446 seniors. So, there are 1,446 possible winners for the car.
37. The flip of the coin is independent of the roll of the die. So, the probability of getting a number
divisible by 3 and a head is the product of the probability of getting a number divisible by 3 and
the probability of getting a head.
The probability of getting a number divisible by 3 is 1/3 and the probability of getting a head is 1/2.
So, the probability of getting a number divisible by 3 and a head is
(1/3)(1/2) = 1/6
38. For every flavor of ice cream, there are 6 different choices of topping Jan could get. So, for each
ice cream flavor, there are 6 possible combinations. Since there are 18 ice cream flavors, multiply
6 possible combinations per flavor times 18 flavors to get the total number of possible
combinations.
18 × 6 = 108 possible combinations
39. Javier bought 4 raffle tickets, and 74 raffle tickets were sold. So, the probability of Javier winning
the raffle is 4/74.
Jackson bought 7 raffle tickets, so the probability of Jackson winning the raffle is 7/74.
Add together the probabilities to find the probability of either Javier or Jackson winning the raffle.
/74 + 7/74 =
4
/74
11
40. Nick gets to choose only 1 hat. There are 14 possible baseball hats he could wear or 11 possible
cowboy hats he could wear. The total number of possible hats he could wear is 14 + 11 = 25 hats.
So, Nick has 25 possible choices.
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