# HW1 ans - STAT 400 Spring 2011 Homework #1 (due Friday,...

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STAT 400 Spring 2011 Homework #1 (due Friday, January 28, by 3:00 p.m.) 1. Suppose that P(A) = 0.40, P(B) = 0.30, P(A B) = 0.20. What is the probability that … a) either A occurs or B occurs (or both); b) B does not occur; c) B occurs and A does not occur; d) neither A nor B occurs; a) P ( A B ) = 0.50 . b) P ( B ' ) = 0.70 . c) P ( B A ' ) = 0.10 . d) P ( A ' B ' ) = 0.50 . 2. Suppose that P ( A ) = 0.40, P ( B ) = 0.50, P ( A B ) = 0.70. Find … a) P ( A B ); b) P ( A ' B ' ); c) P ( A ' B ' ). a) P ( A B ) = P ( A ) + P ( B ) – P ( A B ) 0.7 = 0.4 + 0.5 – P ( A B ) P ( A B ) = 0.2 . b) P ( A ' B ' ) = 1 – P ( A B ) = 1 – 0.7 = 0.3 . c) P ( A ' B ' ) = 1 – P ( A B ) = 1 – 0.2 = 0.8 .

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Suppose P ( A ) = 0.6, P ( B ) = 0.5, P ( C ) = 0.4, P ( A B ) = 0.3, P ( A C ) = 0.2, P ( B C ) = 0.2, P ( A B C ) = 0.1. Find … a) P ( A B ); b) P ( B C ); c) P ( ( A B ) C ' ); d) P ( A ( B C ) ). a) P ( A B ) = P ( A ) + P ( B ) P ( A B ) = 0.6 + 0.5 – 0.3 = 0.8 . b)
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## HW1 ans - STAT 400 Spring 2011 Homework #1 (due Friday,...

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