Solutions 2 Copy.pdf

Solutions 2 Copy.pdf - Homework 2 Solutions Due Wednesday...

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Homework 2 Solutions Due: Wednesday, February 11 Problem 2.56 From past experiences a stockbroker believes that under present economic conditions a cus- tomer will invest in tax-free bonds with a probability of 0.6, will invest in mutual funds with a probability of 0.3, and will invest in both tax-free bonds and mutual funds with a probability of 0.15. At this time, find the probability that a customer will invest (a) in either tax-free bonds or mutual funds but not both; (b) in neither tax-free bonds nor mutual funds. Solution: Consider the events B : customer invests in tax-free bonds, M : customer invests in mutual funds. Then: (a) The event is represented in the Venn diagram below by the shaded area. Its probability P ( ( B M ) ( M B ) ) = P ( B M ) + P ( M B ) = ( P ( B ) - P ( B M ) ) + ( P ( M ) - P ( B M ) ) = P ( B ) + P ( M ) - 2 P ( B M ) = 0 . 6 + 0 . 3 - 2 · 0 . 15 = 0 . 6 . S B M (b) P ( B M ) = 1 - P ( B M ). Since P ( B M ) = P ( B ) + P ( M ) - P ( B M ) = 0 . 6 + 0 . 3 - 0 . 15 = 0 . 75, we have P ( B M ) = 1 - 0 . 75 = 0 . 25. 1
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Problem 2.60 A pair of fair dice is tossed. Find the probability of getting (a) a total of 8; (b) at most a total of 5. Solution: (a) The sample space contains 6 · 6 = 36 equally likely outcomes. The outcomes such that
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