Chapter 7
Review Problems
Problem #1
Use a Venn diagram and the given information
to determine the number of elements in the
indicated region.
n(A) = 35, n(B)= 18, n(A  B) = 45, n(B) = 43
Find n(A  B)
Problem #2
Use a Venn diagram to find the indicated
probability.
P(R) = 0.39, P(S) = 0.34, P(R  S) = 0.21
Find P(R  S)
Problem #3
A card is drawn from a well-shuffled deck
of 52 cards. What is the probability of
drawing a red card that has a value
greater than 5? (Assume Aces are high.)
Problem #4
The age distribution of students at a community
college is given below.
Age (years)
Number of Students
Under 21
525
21 – 25
509
26 – 30
322
31 – 35
115
Over 35
87
A student is selected at random. Find the
probability that the student is at most 25 years
old. Round to the nearest thousandth.
Problem #5
The odds in favor of a football team
winning the Super Bowl are posted as 6:5.
Find the probability that the team will lose
the Super Bowl.
Problem #6
Assume that two gumballs are chosen from a
bag of gumballs with 4 blue, 1 white, 3 green,
and 3 red. Find the probability that:
a.) both gumballs are blue.
b.) the first gumball is red and the second
gumball is green.
Problem #7
In a certain U.S. city, 54.9% of adults are
women. In that city, 16.2% of women and
10.2% of men do not use any means of
public transportation. If an adult is
selected at random from the city, find the
probability that the person does not use
any form of public transportation.
Problem #8
A card is drawn from a well-shuffled deck of 52 cards.
Let A be the event that the card is a spade.
Let B be the event that the card is a ten.
Find: P(A)
P(B)
P(A  B)
Are events A and B independent?
How can you tell?
Problem #9
A person must select one of three bags, each filled
with pennies. One bag contains a gold coin. The
probability of bag A being selected is 0.35, while the
probability of bag B being selected is 0.28. The
probability of finding a gold coin in bag A is 0.3,in bag
B is 0.45, and in bag C is 0.8. A bag is selected at
random.
a.) Draw a tree diagram and label each branch with
the appropriate probabilities.
b.) What is the probability of getting the gold coin?
c.) Given that a person got the gold coin, what is the
probability that bag C contained the coin?
Problem #10
A survey of 200 families showed that 98
had a dog; 57 had a cat; 20 had a dog and
a cat; 51 had neither a dog nor a cat nor a
parakeet; and 2 had a cat, a dog, and a
parakeet.
How many families had a parakeet only?
Answers
1.)
2.)
3.)
4.)
5.)
6.)
7.)
8.)
53
0.82
9/26 or 0.35
0.664
5/11
a.) 6/55 or 0.1091 b.) 9/110 or 0.818
0.135
P(A) = ¼
P(B) = 1/13
P(A  B) = 1/52
Independent events
Because P(A) • P(B) = P(A  B)
9.) b.) 0.527
c.) 0.562
10.) 14