hw1sol - Homework 1 Solution #1 Due 9/12/05 1. Suppose the...

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Homework 1 Solution #1 Due 9/12/05 1. Suppose the sample space S = {1,2,3,4,5,6,7,8,9}, A={1,3,5,7}, B={6,7,8,9}, C={2,4,8} and D = {1,5,9}. A. List the elements of the subsets of S that correspond to the following events (1) A B = {6,8,9} (2) ( A B) C = {8} (3) B C = {1,2,3,4,5,8} (4) ( B C) D = {1,5} 5) A C = {2,4,8} (6) ( A C) D = φ B. Suppose it is given that P(A) = 4 9 ,P(B) = 4 9 ,P(C) = 3 9 ,P(D) = 3 9 ,P(A B) = 1 9 ,P(A C) = 0, P(A D) = 1 9 ,P(B C) = 1 9 ,P(B D) = 1 9 Intersections of three or four of the subsets A, B, C, D have probability zero.(Why?) Find the probability of each of the subsets in part A. (1) P( A B) = P(B) - P(A B) = 4 9 - 1 9 = 3 9 (2) P[( A B) C] = P(B C) - P(A B C) = 1 9 (3) P( B C) = P( B ) + P(C) - P( B C) = 1 - P(B) - P(C) + P(C) + P(B C) = 1 - P(B) + 2P(C) + P(B C) = 1 - 4 9 + 6 9 + 1 9 = 6 9 (4)
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P[( B C) D]
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This note was uploaded on 12/16/2011 for the course CS cs102 taught by Professor Rsharma during the Spring '11 term at IIT Kanpur.

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hw1sol - Homework 1 Solution #1 Due 9/12/05 1. Suppose the...

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