Exam 4: Probability and Probability Models

Three companies produce all the potato chips used by vending machines in public areas in a midwestern state. Company A accounts for 70 percent of the chips, Company B 19 percent, and Company C 11 percent. The probability of the vending company getting an unfilled bag is 2 percent for Company A, 2 percent for Company B, and 4 percent for Company C. Suppose an unfilled bag is found. What is the probability that it came from Company C?

A group has 12 men and 4 women. If 3 people are selected at random from the group, what is the probability that they are all men?

Two percent of the customers of a store buy cigars. Half of the customers who buy cigars buy beer. 25 percent who buy beer buy cigars. Determine the probability that a customer buys beer.

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is a member of the hourly staff, given that the employee is female?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male?

If events A and B are mutually exclusive, then P(A∩B) is always equal to zero.

In a major midwestern university, 55 percent of all undergraduates are female, 25 percent of all undergraduates belong to a Greek organization (fraternity or sorority), and 40 percent of all males belong to a Greek organization. What is the probability that one randomly selected undergraduate will be either a female or belong to a Greek organization?

Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card?

Events that have no sample space outcomes in common, and therefore cannot occur simultaneously, are ________.

Suppose that 60 percent of a company's computer chips are manufactured in Factory A, while 40 percent are produced in Factory B [P(A) = .60 for a randomly selected chip]. The defect rates for the two factories are 35 percent for Factory A and 25 percent for Factory B. Suppose we now know that the randomly selected chip is defective. Find the probability that the defective chip comes from Factory A.

A worldwide personal products manufacturer is working on a new hair care product. In the past, 85 percent of new hair care products introduced by this company have become successful (15 percent have failed). Obviously, the marketing research department plays a large role in the introduction of any new product. Historically, 85 percent of the successful products have a favorable rating from marketing research studies and 20 percent of the unsuccessful products have favorable ratings. For the new hair care product, the marketing unit has issued a favorable rating. What is the probability that the new product will be successful?

Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. If one item is drawn from each container, what is the probability that both items are not defective?

Employees of a local university have been classified according to gender and job type. If an employee is selected at random, what is the probability that the employee is male and salaried staff?

P(AUB) = P(A) + P(B) − P(A∩B) represents the formula for the ________.

A probability may be interpreted as a long-run ________ frequency.

Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will not be accepted at either university?

An auditing firm has developed a set of criteria for determining whether a particular account (and its balance) is in error. Historically, they know that of balances that were in error, 75 percent were regarded as unusual. Assume Company A shows a history of only 10 percent of the account balances being in error and it also shows that 25 percent of the account balances were unusual. What are the states of nature and the experimental outcomes?

A survey is made in a neighborhood of 80 voters. 65 are Democrats and 15 are Republicans. Of the Democrats, 35 are women, while 5 of the Republicans are women. If one subject from the group is randomly selected, find the probability the individual is either a woman or a Democrat.

A subjective probability is a probability assessment that is based on experience, intuitive judgment, or expertise.

An ad agency is developing a campaign to promote a business opening in a new mall development. To develop an appropriate mailing list, they decide to purchase lists of credit card holders from MasterCard and American Express. Combining the lists, they find the following: 40 percent of the people on the list have only a MasterCard and 10 percent have only an American Express card. Another 20 percent hold both MasterCard and American Express. Finally, 30 percent of those on the list have neither card. Suppose a person on the list is known to have a MasterCard. What is the probability that person also has an American Express card?