Geometry
Unit 6 Probability
Study Guide
Name: __________KEY________________ Date: __________________ Period: _______
Directions: Choose the one best answer for the question. Make sure you show all of your work
when solving the problems.
1. A bag contains 6 white, 4 red, 8 green, and 2 blue marbles. Three marbles are drawn at
random from the bag, without replacing the marbles before drawing again. What is the
probability that all of them will be white?
a.
b.
1
57
3
200
c.
d.
3
4
6
20
2. In a particular state, the first character on a license place is always a letter and the last
character is always a digit between 0 and 9. If V represents the set of all license plates
beginning with a vowel and O represents the set of all license plates that end with an odd
number, which license plate belongs in the set V’ ∩ O’ ?
a.
c.
b.
d.
3. Which of the following events are independent given P(A), P(B), and P(A and B)?
a. P(A)= 0.43; P(B) = 0.53; P(A and B) = 1
b. P(A)= 0.33; P(B) = 0.33; P(A and B) = 0.66
c. P(A)= 0.18; P(B) = 0.27; P(A and B) = 0.049
d. P(A)= 0.25; P(B) = 0.25; P(A and B) = 0.50
Geometry
Unit 6 Probability
Study Guide
4. In a baseball game, a shutout is a game where the winning team does not allow the other
team to score runs. If the set W represents all wins, and the set S represents all shutouts,
which set describes the set of wins that were shutouts?
a. W’ ∩ S
c. W ∩ S
b. W’ ∪ S
d. W ∪ S’
5. Henry rolls two fair dice. If he rolls a 4 on one of the dice, what is the probability that
the sum of the numbers facing up on both dice is greater than or equal to 7?
a. 0.42
c. 0.17
b. 0.58
d. 0.13
1
3
6. For two events A and B, (A) = 4 , and P(B|A) = 2 . What is P(B)?
a.
b.
c.
1
3
2
3
3
8
d. Not enough information to determine
7. Two tests were administered in Mrs. Simmons class. 40% of the students passed both
tests and 55% of the students passed the first test. What percent of students passed the
second test given that they passed the first test?
a. 22%
c. 42%
b. 73%
d. 58%
8. In a survey of 450 people, 200 of whom are female, it was found that 225 preferred
comedy movies including 99 males.
Males
Females
Totals
Comedy
99
126
225
Scary
75
35
110
Action
76
39
115
Totals
250
200
450
What is the probability that an individual will choose a male given they like comedy?
a. 0.40
c. 0.22
b. 0.90
d. 0.44
Geometry
Unit 6 Probability
Study Guide
9. The table below shows the type and color of 20 pieces placed in a bag. If a piece is
selected at random from the bag is white, what is the probability it is a chip?
Type and Color of Pieces
a.
b.
1
4
1
2
Chips
Balls
Blue
3
6
White
5
2
Red
2
2
c.
d.
5
7
7
10
10. Tickets are numbered 1 to 24 and put into a cup. The numbers are then mixed up and a
ticket is drawn at random. What is the probability of drawing a number that is a multiple
of 3 or 4?
1
c. 0
a.
12
b.
1
d. 1
2
11. Using the frequency table below, determine the probability of randomly selecting a
person who skates or a female.
a.
b.
19
26
11
16
c.
d.
11
14
77
208
Geometry
Unit 6 Probability
Study Guide
12. If a card is drawn from a deck of four cards labeled A – D and the spinner is spun once,
what is the probability of drawing a C and spinning an even number?
A
a.
b.
5
32
3
32
B
C
c.
d.
D
5
8
3
8
13. When looking at the relationship between the events “owns a skateboard” and “likes to
read”, if the events are independent, then the probability:
P(likes to read|owns a skateboard) is equal to _______.
a. P(owns a skateboard)
b. P(likes to read)
c. P(likes to read) + P(owns a skateboard)
d. P(likes to read) x P(owns a skateboard)
14. Mr. Bruner surveyed 150 men and 185 women about their vehicles. Of those surveyed,
75 men and 105 women said they own a red vehicle. If a person is chosen at random
from those surveyed, what is the probability of choosing a woman or a person that owns a
red vehicle?
a.
b.
52
67
105
185
c.
d.
105
180
47
67
Geometry
Unit 6 Probability
Study Guide
15. Using the spinners below, find the probability of spinning a 2 and a vowel.
a.
b.
1
4
1
3
c.
d.
1
12
7
12
16. A new Spiderman Visa has been issued to 1000 customers. Of these customers, 500 hold
a MasterCard, 500 hold a Discover card, and 50 hold a MasterCard and a Discover card.
What is the probability that a customer chosen at random holds a MasterCard, given that
the customer holds a Discover card?
a.
b.
1
10
1
4
c.
d.
1
2
1
50
17. A local restaurant asked 1000 people, “Did you cook dinner last night?” The results of
the survey are shown in the table below.
Determine what the probability is of a person chosen at random from the 1000 surveyed
was a male and did not cook dinner last night.
a.
b.
221
500
327
1000
c.
d.
23
200
81
200
Geometry
Unit 6 Probability
Study Guide
18. If P(E) is the probability that an event will occur, which of the following statement(s) are
true:
1
1
i. P(E) = 2 , ii. P(E) = 4 ,
iii. P(E) = -1,
iv. P(E) = 1
a. i and ii
c. i, ii, and iv
b. iii
d. i and iv
19. At McDonalds, everyone drinks sweet tea. Let R equal the event that a randomly
selected customer puts Raspberry flavoring in their tea. Let L equal the event that a
randomly selected customer puts lemon in their tea. Suppose that after months of
collecting data, McDonalds has estimated the following probabilities: P(R) = 0.33,
P(L) = 0.44, and P(R or L) = 0.55
Estimate P(R and L) in context of this problem.
a. 0.5
c. 0.3
b. 0.4
d. 0.2
20. The probabilities of an adult male having high blood pressure and/or high cholesterol are
given in the table below. What is the probability that a randomly selected male has
normal blood pressure or normal cholesterol?
a. 0.90
c. 0.53
b. 0.70
d. 1.45
21. This Venn diagram below shows the names of students in Mrs. Hill’s class that are older
than 8, has blonde hair, and are boys. Let BH represent blonde hair, O represent older
than 8 and B represent boy. Use the diagram to answer the following questions:
Geometry
Unit 6 Probability
Study Guide
a. Find the BH ∩ O. What does this set represent?
b. Find BH ∪ B. What does this set represent?
c. Find (BH ∪ O)’. What does this set represent?
22. In New Manchester High School, the probability that a student is active in sports is 65%.
The probability that a student is between the ages of 14 and 17 is 88%. The probability
that the student is active in sports and is between the ages of 14 and 17 is 57%. Are the
event independent or not independent or not and how do you know?
23. Use the two way frequency below to calculate the probability for each statement.
Event Y
Event Z
Total
Event W
12
24
36
Event X
36
28
64
Total
48
52
100
Geometry
Unit 6 Probability
Study Guide
a. Calculate P(X|Y)
b. Calculate P(Z|W)
c. Calculate P(Z|X)
d. Will the P(Z|W) and P(W|Z) give you the same result? Explain why or why not.
24. The table below gives data on passengers who were aboard the Titanic when it struck the
iceberg on April 15, 1912. Use this table to answer the following questions:
a. Are the events “passenger survived” and “passenger in second class”
independent? Support your answer using appropriate probability calculations.
b. Are the events “passenger did not survive” and “passenger in first class”
independent? Support your answer using appropriate probability calculations.
c. Did all of the passengers have an equal chance of surviving aboard the Titanic?
Support your answer using appropriate probability calculations.