STAT 400 hw1_ans

# STAT 400 hw1_ans - STAT 400 MATH 463 Fall 2011...

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STAT 400 / MATH 463 Fall 2011 Homework #1 (due Friday, September 2, by 3:00 p.m.) 1. Suppose that P(A) = 0.60, P(B) = 0.40, P(A B) = 0.30. 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 ) = 0.70 . b) P ( B ' ) = 0.60 . c) P ( B A ' ) = 0.10 . d) P ( A ' B ' ) = 0.30 . 2. 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) P ( B C ) = P ( B ) + P ( C ) P ( B C ) = 0.5 + 0.4 – 0.2 = 0.7 .

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c) P ( ( A B ) C ' ) = 0.5 . d) P ( A ( B C ) ) = 0.7 . 3. Suppose a baseball player steps to the plate with the intention of trying to “coax” a base on balls by never swinging at a pitch. The umpire, of course, will necessarily call each pitch either a ball (B) or a strike (S). What outcomes make up the event A, that a batter walks on the sixth pitch? Note: A batter “walks” if the fourth ball is called before the third strike. S S B B B B B S S B B B B B S S B B S B S B B B B S B S B B B B S B S B S B B S B B B S B B S B B B B S S B S B B B S B 4. Consider a “thick” coin with three possible outcomes of a toss ( Heads , Tails , and Edge ) for which Heads and Tails are equally likely, but Edge is seven times less likely than Heads . What is the probability of Heads ?
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