CHAPTER 6 SECTION 3: PROBABILITY

MULTIPLE CHOICE

129. If P(A) = 0.84, P(B) = 0.76, and P(A or B) = 0.90, then P(A and B) is:
a. 0.06
b. 0.14
c. 0.70
d. 0.83
130. If P(A) = 0.20, P(B) = 0.30, and P(A and B) = 0, then A and B are:
a. dependent events
b. independent events
c. mutually exclusive events
d. complementary events
131. If P(A) = 0.65, P(B) = 0.58, and P(A and B) = 0.76, then P(A or B) is:
a. 1.23
b. 0.47
c. 0.24
d. None of these choices.
132. Suppose P(A) = 0.35. The probability of the complement of A is:
a. 0.35
b. 0.65
c. 0.35
d. None of these choices.
133. If the events A and B are independent with P(A) = 0.30 and P(B) = 0.40, then the probability that both
events will occur simultaneously is:
a. 0
b. 0.12
c. 0.70
d. Not enough information to tell.
134. If events A and B are independent then:
a. P(A and B) = P(A) * P(B)
b. P(A and B) = P(A) + P(B)
c. P(B|A) = P(A)
d. None of these choices.
135. Two events A and B are said to be mutually exclusive if:
a. P(A|B) = 1
b. P(A|B) = P(A)
c. P(A and B) =1
d. P(A and B) = 0
136. Which of the following statements is always correct?
a. P(A and B) = P(A) * P(B)
b. P(A or B) = P(A) + P(B)
c. P(A) = 1  P(Ac)
d. None of these choices.

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137. If A and B are mutually exclusive events, with P(A) = 0.20 and P(B) = 0.30, then the probability that
both events will occur simultaneously is:
a. 0.50
b. 0.06
c. 0
d. None of these choices.
138. If A and B are independent events with P(A) = 0.60 and P(B) = 0.70, then P(A or B) equals:
a. 1.30
b. 0.88
c. 0.42
d. Cannot tell from the given information.
139. If A and B are mutually exclusive events with P(A) = 0.30 and P(B) = 0.40, then P(A or B) is:
a. 0.10
b. 0.12
c. 0.70
d. None of these choices
140. If A and B are any two events with P(A) = .8 and P(B|A) = .4, then P(A and B) is:
a. .40
b. .32
c. 1.20
d. None of these choices.
141. If A and B are any two events with P(A) = .8 and P(B|Ac) = .7, then P(Ac and B) is
a. 0.56
b. 0.14
c. 1.50
d. None of these choices.
TRUE/FALSE

142. If the event of interest is A, the probability that A will not occur is the complement of A.

143. Assume that A and B are independent events with P(A) = 0.30 and P(B) = 0.50. The probability that
both events will occur simultaneously is 0.80.

144. Two events A and B are said to be independent if P(A) = P(A|B).

145. Two events A and B are said to be independent if P(A|B) = P(B).

146. Two events A and B are said to be independent if P(A|B) = P(B|A).

147. Two events A and B are said to be mutually exclusive if P(A and B) = 1.0.

148. If events A and B have nonzero probabilities, then they can be both independent and mutually
exclusive.

149. The probability of the union of two mutually exclusive events A and B is 0.

150. If A and B are two independent events with P(A) = 0.9 and P(B|A) = 0.5, then P(A and B) = 0.45.

151. Jim and John go to a coffee shop during their lunch break and toss a balanced coin to see who will pay.
The probability that John will pay three days in a row is 0.125.

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152. When A and B are mutually exclusive, P(A or B) can be found by adding P(A) and P(B).

153. If P(A and B) = 1, then A and B must be mutually exclusive.

154. Events A and B are either independent or mutually exclusive.

155. If P(B) = .7 and P(B|A) = .4, then P(A and B) must be .28.

156. If P(B) = .7 and P(A|B) = .7, then P(A and B) = 0.

COMPLETION

157. The ____________________ rule says that P(Ac) = 1  P(A).

158. The ____________________ rule is used to calculate the joint probability of two events.

159. If A and B are ____________________ events, the joint probability of A and B is the product of the
probabilities of those two events.

160. The ____________________ rule is used to calculate the probability of the union of two events.

161. If A and B are ____________________ then the probability of the union of A and B is the sum of their
individual probabilities.

162. The first set of branches of a probability tree represent ____________________ probabilities.

163. The second set of branches of a probability tree represent ____________________ probabilities.

164. When you multiply a first level branch with a second level branch on a probability tree you get a(n)
____________________ probability.

165. If two events are complements, their probabilities sum to ____________________.

166. If two events are mutually exclusive their joint probability is ____________________.

SHORT ANSWER

167. Suppose A and B are two independent events for which P(A) = 0.20 and P(B) = 0.60.

a. Find P(A and B).

b. Find P(A or B).

University Job

A Ph.D. graduate has applied for a job with two universities: A and B. The graduate feels that she has a
60% chance of receiving an offer from university A and a 50% chance of receiving an offer from
university B. If she receives an offer from university B, she believes that she has an 80% chance of
receiving an offer from university A. Let A = receiving an offer from university A, and let B =
receiving an offer from university B.

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168. {University Job Narrative} What is the probability that both universities will make her an offer?

169. {University Job Narrative} What is the probability that at least one university will make her an offer?

170. {University Job Narrative} If she receives an offer from university B, what is the probability that she
will not receive an offer from university A?

171. Suppose P(A) = 0.50, P(B) = 0.40, and P(B|A) = 0.30.

a. Find P(A and B).

b. Find P(A or B).
c. Find P(A|B).

172. A survey of a magazine's subscribers indicates that 50% own a house, 80% own a car, and 90% of the
homeowners also own a car. What proportion of subscribers:

a. own both a car and a house?

b. own a car or a house, or both?
c. own neither a car nor a house?

173. Suppose A and B are two mutually exclusive events for which P(A) = 0.30 and P(B) = 0.40.

a. Find P(A and B).

b. Find P(A or B).
c. Are A and B independent events? Explain using probabilities.

174. Suppose P(A) = 0.30, P(B) = 0.50, and P(B|A) = 0.60.

a. Find P(A and B).

b. Find P(A or B).
c. Find P(A|B).

175. Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A or B) = 0.30? Explain.

176. A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1%
of the population. The firm has announced that 95% of those infected will show a positive test result,
while 98% of those not infected will show a negative test result.

a. What proportion of people don't have the disease?

b. What proportion who have the disease test negative?
c. What proportion of those who don't have the disease test positive?
d. What proportion of test results are incorrect?
e. What proportion of test results are correct?

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 Marital Status

An insurance company has collected the following data on the gender and marital status of 300 customers.
Marital Status
Gender Single Married Divorced
Male 25 125 30
Female 50 50 20

Suppose that a customer is selected at random.

177. {Marital Status Narrative} Find the probability that the customer selected is female or divorced.

178. {Marital Status Narrative} Are gender and marital status mutually exclusive? Explain using
probabilities.

179. {Marital Status Narrative} Is marital status independent of gender? Explain using probabilities.

Company Bids
A construction company has submitted bids on two separate state contracts, A and B. The company
feels that it has a 60% chance of winning contract A, and a 50% chance of winning contract B.
Furthermore, the company believes that it has an 80% chance of winning contract A if it wins contract
B.

180. {Company Bids Narrative} What is the probability that the company will win both contracts?

181. {Company Bids Narrative} What is the probability that the company will win at least one of the two
contracts?

182. {Company Bids Narrative} If the company wins contract B, what is the probability that it will not win
contract A?

183. {Company Bids Narrative} What is the probability that the company will win at most one of the two
contracts?

184. {Company Bids Narrative} What is the probability that the company will win neither contract?

House Sales and Interest Rates

The probability that house sales will increase in the next 6 months is estimated to be 0.30. The
probability that the interest rates on housing loans will go up in the same period is estimated to be
0.75. The probability that house sales or interest rates will go up during the next 6 months is estimated
to be 0.90.

185. {House Sales and Interest Rates Narrative} What is the probability that both house sales and interest
rates will increase during the next six months?

186. {House Sales and Interest Rates Narrative} What is the probability that neither house sales nor interest
rates will increase during the next six months?

187. {House Sales and Interest Rates Narrative} What is the probability that house sales will increase but
interest rates will not during the next six months?

This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold,
copied, or distributed without the prior consent of the publisher.