Probability and Predictions Study Guide
Identify the choice that best completes the statement or answers the question.
A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a marble at random
without looking. Find the probability of each event. Write your answer as a fraction in simplest form.
____
____
____
____
1. P(red)
A
C
B
D
2. P(red or white)
A
C
B
D
3. P(blue or purple)
A
C
B
D
4. P(not white)
A
C
B
D
During lunch at Urbana Middle School today, several students have brought their lunch from home and several students
are ordering a school lunch as shown in the table. Suppose one student is randomly selected during lunch time. Find the
probability of each event. Write as a fraction in simplest form.
Brought lunch from home
Order school lunch
6th Graders
7th Graders
8th Graders
____
55
45
32
35
33
5. P(7th grader or 8th grader)
A
C
B
D
____
6. A bag of sweets contains 24 gummy bears and 39 orange slices. One sweet is taken at random from the bag. What is the
probability of picking a gummy bear?
____
____
____
A
C
B
D
13
21
7. A number cube is tossed and the spinner below is spun. Find P(greater than 4 and A).
A
1
3
C
2
9
B
4
9
D
1
6
8. One bag contains 7 red chips and 5 yellow chips. Another bag contains 5 red chips and 2 yellow chips. A chip is
drawn from each bag. What is the probability that both chips are yellow?
A
25
84
C
1
6
B
5
12
D
5
42
9. What is the probability of rolling two number cubes and getting a number greater than 2 on each cube.
A
C 1
B
D
Glenn surveyed 40 of his classmates to determine their favorite cafeteria food. The results of his survey are
shown in the table.
Favorite Food
Number of
Students
Meatloaf
4
Tacos
5
Hamburgers
9
Pizza
18
Fish
4
____ 10. What is the probability of pizza being a student’s favorite cafeteria food?
A
C
B
D
____ 11. What is the probability of tacos being a student’s favorite cafeteria food?
A
C
B
D
____ 12. Suppose there are 200 students in the cafeteria during lunch. How many students would you expect to choose
hamburgers as their favorite cafeteria food?
A 50
B 9
C 45
D 36
____ 13. An automobile manufacturer makes 3 different car models. Each car comes in one of 5 different interior styles.
Each model also comes in 17 different colors. A car dealer wants to order one of each kind of car to have on his
lot. Find the probability of randomly selecting a car from the different models using Fundamental Counting
Principle?
A
C
B
D
Matthews has a bag containing 3 English, 2 Math, and 5 Science books. Find the probability of randomly
selecting an English book.
A 3/10
C 5/6
B 4/5
D 2/9
Find the probability of choosing a mountain bike that come in five colors and three styles.
A 5/6
C 1/15
B 1/14
D 5/12
Use the Fundamental Counting Principle to find the total number of outcomes in each situation.
____ 16. rolling a number cube and tossing a nickel
A 6
B 8
C 24
D 12
____ 17. choosing a tuna, turkey, or cheese sandwich; on wheat or white bread; with a side of potato chips, corn chips, or baked
potato
A 18
B 24
C 8
D 9
____ 18. choosing a number from 1 to 15 and a vowel from the word COUNTING
A 120
B 45
C 90
D 55
Solve.
____ 19. How many 4-digit codes can be created if no digit can be repeated?
A 256
C 5,040
B 10,000
D 2,520
____ 20. There are 12 swimmers in a free style race, with prizes going to the first, second, and third place finishers. In how many
ways can the prizes be awarded?
A 1,320
B 1,728
C 2,640
D 884
____ 21. Emily has 10 books, but she only has room on her bookshelf for 5 of them. In how many ways can she arrange 5 of the
books on her shelf?
A 15,120
B 100,000
C 30,240
D 35,280
For each situation, make a tree diagram or table to show the sample space. Then give the total number of
outcomes.
____ 22. tossing a nickel and tossing a quarter
A 2
B 4
C 6
D 8
____ 23. picking a number from 1 to 4 and choosing the color red, green, or yellow
A 6
B 9
C 12
D 24
____ 24. choosing either turkey or ham on wheat or rye bread
A 2
B 8
C 4
D 12
____ 25. Find the sample space using the table below.
Shirt
yellow shirt
green shirt
Trouser
white trouser
black trouser
A yellow shirt, white trouser
C
yellow shirt, black trouser
green shirt, white trouser
green shirt, black trouser
yellow shirt, white trouser
green shirt, black trouser
green shirt, white trouser
green shirt, black trouser
D
B
yellow shirt, white trouser
yellow shirt, black trouser
green shirt, white trouser
green shirt, white trouser
yellow shirt, white trouser
yellow shirt, black trouser
yellow shirt, white trouser
green shirt, black trouser
Probability and Predictions Pre Test
Answer Section
MULTIPLE CHOICE
1. ANS: D
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
Double check your work and try again.
Be sure to write your answer in simplest form.
How many favorable outcomes are there? How many total outcomes are there?
Correct!
PTS:
OBJ:
TOP:
2. ANS:
1
DIF: Basic
REF: Probability
8-1.1 Find the probability of a simple event.
Find the probability of a simple event.
A
KEY: Probability | Simple events
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
Correct!
Double check your work and try again.
Be sure to write your answer in simplest form.
How many favorable outcomes are there? How many total outcomes are there?
PTS:
OBJ:
TOP:
3. ANS:
1
DIF: Average
REF: Probability
8-1.1 Find the probability of a simple event.
Find the probability of a simple event.
B
KEY: Probability | Simple events
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
Double check your work and try again.
Correct!
How many favorable outcomes are there? How many total outcomes are there?
Be sure to write your answer in simplest form.
PTS:
OBJ:
TOP:
4. ANS:
1
DIF: Average
REF: Probability
8-1.1 Find the probability of a simple event.
Find the probability of a simple event.
C
KEY: Probability | Simple events
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
This is the probability of drawing a white marble. What is the probability that a white
marble is not drawn?
Double check your work and try again.
Correct!
How many marbles are not white? Compare this number with the total number of possible
outcomes.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.1 Find the probability of a simple event.
TOP: Find the probability of a simple event.
KEY: Probability | Simple events
5. ANS: B
Write the number of favorable outcomes over the total number of possible outcomes and simplify.
Feedback
A
B
C
D
How many students are either a 7th grader or an 8th grader?
Correct!
Double check your work and try again.
Be careful when simplifying your fraction. Try again.
PTS:
OBJ:
TOP:
6. ANS:
1
DIF: Average
REF: Probability
8-1.1 Find the probability of a simple event.
Find the probability of a real-world simple event.
B
P(gummy
bear)
KEY: Probability | Simple events
=
=
The probability of picking a gummy bear is
.
Feedback
A
B
C
D
Divide both the numerator and denominator by the greatest common factor.
Correct!
This is the probability of picking an orange slice, without simplification.
This is the probability of picking an orange slice.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.1 Find the probability of a simple event.
TOP: Find the probability of a real-world simple event.
KEY: Probability | Simple events
7. ANS: D
The probability of two independent events can be found by multiplying the probability of the first event by the
probability of the second event. For example:
Feedback
A
B
C
D
How do you find compound probabilities?
Did you find the probabilities of each event and multiply?
Did you add the numerators and denominators?
Correct!
PTS: 1
DIF: Average
REF: Compound Events
OBJ: 8-2.1 Find the probability of independent events.
TOP: Find the probability of independent and dependent events.
KEY: Independent events | Dependent events
8. ANS: D
The probability of two independent events can be found by multiplying the probability of the first event by the
probability of the second event.
If there are 5 red and 4 yellow in the first bag, and 3 red and 9 yellow in the second for example:
Feedback
A
B
C
D
That is the probability that the one from the first bag is yellow and from the second is red.
That is the probability that both are red.
That is the probability that the one from the first bag is red and the second bag is yellow.
Correct!
PTS:
OBJ:
TOP:
KEY:
9. ANS:
1
DIF: Average
REF: Compound Events
8-2.2 Find the probability of dependent events.
Find the probability of independent and dependent events.
Independent events | Dependent events
A
Feedback
A
B
C
D
Correct!
That is the probability of rolling less than two on both.
That would mean you would always roll greater than two.
That is the probability of rolling greater than two with just one cube.
PTS: 1
DIF: Average
REF: Compound Events
OBJ: 8-2.1 Find the probability of independent events.
TOP: Find the probability of independent and dependent real-world events.
KEY: Independent events | Dependent events
10. ANS: D
Write the number of students who voted for pizza over the total number of students surveyed and simplify.
Feedback
A
B
C
D
Be sure to write your answer in simplest form.
Divide the number of students who voted for pizza by the total number of students
surveyed.
How many students voted for pizza? How many students were surveyed?
Correct!
PTS: 1
DIF: Average
REF: Predictions
OBJ: 8-3.1 Find experimental probabilities.
TOP: Find experimental probabilities.
KEY: Experimental probability | Theoretical probability
11. ANS: A
Write the number of students who voted for pizza over the total number of students surveyed and simplify.
Feedback
A
B
C
D
Correct!
Divide the number of students who voted for tacos by the total number of students
surveyed.
How many students voted for tacos? How many students were surveyed?
Double check your work and try again.
PTS: 1
DIF: Average
REF: Predictions
OBJ: 8-3.1 Find experimental probabilities.
TOP: Find experimental probabilities.
KEY: Experimental probability | Theoretical probability
12. ANS: C
Students can set up a proportion to solve the problem. One ratio is the number of students who voted for
hamburgers over the number of students surveyed. The other ratio is the number of students who would choose
hamburgers over the number of students in the cafeteria.
Feedback
A
B
C
D
Double check your work and try again.
This is how many students out of 40 chose hamburgers. How many students out of 200
would you expect to choose hamburgers?
Correct!
Be careful when solving your proportion. Try again.
PTS: 1
DIF: Average
TOP: Find theoretical probabilities.
13. ANS: C
car models
interior styles
3
5
REF: Predictions
OBJ: 8-3.2 Find theoretical probabilities.
KEY: Experimental probability | Theoretical probability
colors
17
total
=
255
Fundamental
Counting Principle.
There are 255 cars ordered by the dealer. Out of 255 possible outcomes, only 1 is favorable. So, the probability
of randomly selecting a car from different models is
.
Feedback
A
B
C
D
Multiply the denominator by the total number of models and colors.
Multiply the denominator by the total number of interior styles and colors.
Correct!
Multiply the denominator by the total number of interior styles and models.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.6 Use multiplication to find probabilities.
TOP: Use multiplication to find probabilities.
KEY: Multiplication | Probabilities
14. ANS: D
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
6(2) = 12
Feedback
A
B
C
D
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
Double check your work and try again.
How many ways can you roll a number cube? How many ways can you toss a nickel?
Correct!
PTS: 1
DIF: Basic
REF: Probability
OBJ: 8-1.5 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes and find probabilities.
KEY: Probability | Counting
15. ANS: A
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
3(2)(3) = 18
Feedback
A
B
C
D
Correct!
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
How many possible outcomes are there for each of the three choices?
Double check your work and try again.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.5 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes and find probabilities.
KEY: Probability | Counting
16. ANS: B
Multiply the number of outcomes for each event to find the total number of outcomes in the sample space.
15(3) = 45
Feedback
A
How many vowels are there in the word COUNTING?
B
C
D
Correct!
Double check your work and try again.
Multiply the number of outcomes for each event to find the total number of outcomes in
the sample space.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.5 Use multiplication to count outcomes.
TOP: Use multiplication to count outcomes and find probabilities.
KEY: Probability | Counting
17. ANS: C
There are 10 ways to pick the first digit, 9 ways to pick the second digit, 8 ways to pick the third digit, and 7
ways to pick the fourth digit.
10 · 9 · 8 · 7 = 5,040
Feedback
A
B
C
D
How many ways are there to pick the first digit, the second digit, and so on?
Double check your work and try again.
Correct!
Be careful when computing the multiplication. Try again.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.8 Find the number of permutations of a set of objects.
TOP: Find the number of permutations of a set of objects and find probabilities.
KEY: Probability | Permutation
18. ANS: A
There are 12 ways to pick the first swimmer, 11 ways to pick the second swimmer, and 10 ways to pick the third
swimmer.
12 · 11 · 10 = 1,320
Feedback
A
B
C
D
Correct!
How many ways are there to pick the first swimmer, the second swimmer, and the third
swimmer?
Be careful when computing the multiplication. Try again.
Double check your work and try again.
PTS: 1
DIF: Average
REF: Probability
OBJ: 8-1.8 Find the number of permutations of a set of objects.
TOP: Find the number of permutations of a set of objects and find probabilities.
KEY: Probability | Permutation
19. ANS: C
There are 10 ways to pick the first book, 9 ways to pick the second book, and so on.
10 · 9 · 8 · 7 · 6 = 30,240
Feedback
A
B
C
D
Be careful when computing the multiplication.
How many ways are there to pick the first book, the second book, and so on?
Correct!
Double check your work and try again.
PTS:
OBJ:
TOP:
KEY:
20. ANS:
1
DIF: Average
REF: Probability
8-1.8 Find the number of permutations of a set of objects.
Find the number of permutations of a set of objects and find probabilities.
Probability | Permutation
B
There are four possible outcomes: HH, HT, TH, and TT.
Feedback
A
B
C
D
List all of the possible outcomes for the first coin. Then list all of the possibilities for the
second coin, given the result of the first coin.
Correct!
List all of the possible outcomes to make sure they are all unique.
Double check your work and try again.
PTS: 1
DIF: Basic
REF: Probability
TOP: Find sample spaces and probabilities.
21. ANS: C
OBJ: 8-1.2 Find sample spaces.
KEY: Probability | Tree diagram
There are twelve possible outcomes: 1R, 1G, 1Y, 2R, 2G, 2Y, 3R, 3G, 3Y, 4R, 4G, and 4Y.
Feedback
A
B
C
D
List all of the possible outcomes for the number. Then branch off each number to list all
of the possible outcomes for the color.
Double check your work and try again.
Correct!
List all of the possible outcomes to make sure they are all unique.
PTS: 1
DIF: Average
REF: Probability
TOP: Find sample spaces and probabilities.
22. ANS: C
OBJ: 8-1.2 Find sample spaces.
KEY: Probability | Tree diagram
There are four possible outcomes: turkey on wheat, turkey on rye, ham on wheat, and ham on rye.
Feedback
A
B
C
D
List all of the possible outcomes for the type of meat. Then branch off to list all of the
possible outcomes for the type of bread.
List all of the possible outcomes to make sure they are all unique.
Correct!
Double check your work and try again.
PTS: 1
DIF: Basic
REF: Probability
TOP: Find sample spaces and probabilities.
23. ANS: A
Make a tree diagram that shows all of the possible outcomes.
OBJ: 8-1.2 Find sample spaces.
KEY: Probability | Tree diagram
Sample Space
white trouser
yellow shirt, white trouser
black trouser
yellow shirt, black trouser
yellow shirt
white trouser
green shirt, white trouser
black trouser
green shirt, black trouser
green shirt
Feedback
A
B
C
D
Correct!
Second and fourth sample spaces are same.
Third and fourth sample spaces are same.
First and third sample spaces are same.
PTS: 1
DIF: Average
REF: Probability
TOP: Find sample spaces and probabilities.
OBJ: 8-1.2 Find sample spaces.
KEY: Sample space