11. Let A be an event that a person's primary method of transportation to and from work is an automobile and B be an event that a person's primary method of transportation to and from work is a bus. Suppose that in a large cityP(A) = 0.45 and P(B) = 0.35.
a. Are events A and B mutually exclusive? What is the probability that a person uses an automobile or a bus in going to and from work?
b. Find the probability that a person's primary method of transportation is some means other than it bus.
17. Interested in learning more about its fans, the marketing office of the Arena Football
League (AFL) conducted a survey at one of its games. The survey had 989 respondents:
759 males and 230 females. Out of the 989 total respondents, 196 stated that they had attended multiple AFL games. Of these 196 fans that had attended multiple games, 177 were male. Using this survey information, answer the following questions.
a. What is the probability that a randomly selected fan has attended multiple games?
b. Given that a randomly selected fan has attended multiple games, what is the probability of this person being male?
c. What is the probability of a randomly selected fan being male and having attended multiple games?
d. Given that a randomly selected fan is male, what is the probability that this person has attended multiple games?
e. what is the probability that a randomly selected fan is male or has attended multiple games?21. A consulting firm submitted a bid for a large research project. The firm's management initially felt there was a 50/50 chance of getting the bid. However, the agency to which the bid was submitted subsequently requested additional information on the bid. Experience indicates that on 75% of the successful bids and 40% of the unsuccessful bids the agency requested additional information,
a. What is the prior probability that the bid will be successful (i.e., prior to receiving the request for additional information)?
b. What is the conditional probability of a request for additional information given that the bid will ultimately be successful?
c. Compute a posterior probability that the bid will be successful given that a request for additional information has been received.
23. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.
P (high quality oil) = 0.50
P (medium quality oil) = 0.20
P (no oil) = 0.30
a. What is the probability of finding oil?
b. After 200 feet of drilling on the first well, a soil test is made. The probabilities of finding the particular type of soil identified by the test are
P (soil high quality oil) = 0.20
P (soil medium quality oil) = 0.20
P (soil no oil) = 0.30
How should the firm interpret the soil test? What are the revised probabilities, and what is the new probability of finding oil?