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Unformatted text preview: m # 3.17 a. Compute P(A1 or A2 ) b. Compute P(A2 or B2 ) c. Compute P(A3 or B1 ) Problem # 3.18 A firm has classified its customers in two ways: (1) according t whether the account is overdue and (2) whether the account is new (less than 12 months) or old. An analysis of the firm’s records provided the input for the following table of joint probabilities. Overdue Not Overdue New .06 .13 Old .52 .29 One account is randomly selected. a. If the account is overdue, what is the probability that it is new? b. If the account is new, what is the probability that it is overdue? c. Is the age of the account related to whether it is overdue? Explain. 5 Problem # 3.19 A and B are mutually exclusive events, with P(A) = 0.2 and P(B) = 0.3. a. Find P(A|B) b. Are A and B independent events? Problem # 3.20 For two events, A and B, P(A) = .4, P(B) = .2, and P(A∩ B) = .1. a. Find P (A|B). b. Find P (B|A). c. Are A and B independent events? Problem # 3.21 An investor believes that on a day when the Dow Jones industrial Average (DJIA) increase, the probability that the NASDAQ also increases is 77%. If the investor believes that there is a 60% probability that the DJIA will increase tomorrow, what is the probability that the NASDAQ will increase as well? Problem # 3.22 Calculate the marginal probabilities from the following table of joint probabilities. Table 3.3 A1 A2 B1 0.4 0.3 B2 0.2 0.1 Problem # 3.23 Refer to 3 ­22 problem, Determine P( A1 | B1 ) . Determine P( A2 | B1 ) . 6 Did you answers to parts a and b sum to 1? Is this a coincidence? Explain Problem #3.24 Refer to 3 ­22. Calculate the following probabilities. a. P(A1|B2) = b. P(B2|A1) = c. Did you expect the answer to part a and b to be reciprocals? That is, did you expect that P (A1|B2) = 1/ P (B2|A1)? Why is this impossible (unless both probabilities are 1)? Problem #3.25 In 2008, McDonald’s had 31,967 restaurants system wide. Of these, 21,328 were operated by franchises, 6,502 by the company, and 4,137 by affiliates. What is the probability that a randomly selected McDonald’s restaurant is operated by either a franchisee or an affiliate? Source: McDonald’s Corporation, 2008 Annual Report, p.44. Problem # 3.26 (Attempt this problem on a separate sheet of paper as it is very long) The U.S. Bureau of Justice released the following probabilities for those arrested for committing various felony crimes in...
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This note was uploaded on 09/30/2013 for the course COMM 215 taught by Professor Ghatri during the Fall '08 term at Concordia Canada.

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