131A_1_EE131AF06MidTermSolution

131A_1_EE131AF06MidTermSolution - Solution of Midterm Exam,...

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Solution of Midterm Exam, EE 131A October 30, 2006 Problem 1 (20 pts) Urn A contains 3 red and 3 black balls, urn B contains 4 red and 6 black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be of the same color? Solution: Let R and B be the events that both balls are red and black, respectively. Then the desired event is R B (a disjoint union), and P [ R B ] = P [ R ] + P [ B ] = (3)(4) (6)(10) + (3)(6) (6)(10) = 1 2 . Problem 2 (20 pts) A box contains m white and n black balls. Suppose k balls are drawn (with replacement). Find the probability of drawing at least one white ball. Solution: We can consider this experiment as a Bernoulli trail with “drawing a white ball” as the “success.” Then the probability of “success” is equal to p = m m + n ; and P [ at least one white ball ] = 1 - P [ all back balls ] = 1 - p k k P p 0 (1 - p ) k = 1 - p 1 - m m + n P k = 1 - p n m + n P k .
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This note was uploaded on 06/09/2010 for the course EE 131A taught by Professor Lorenzelli during the Spring '08 term at UCLA.

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131A_1_EE131AF06MidTermSolution - Solution of Midterm Exam,...

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