# 08_30ans - STAT 400 BL1 Examples for Fall 2011 Events A and...

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STAT 400 – BL1 Examples for 08/30/2011 Fall 2011 Events A and B are independent if and only if P ( B A ) = P ( B ) P ( A B ) = P ( A ) P ( A B ) = P ( A ) P ( B ) Note that if two events, A and B, are mutually exclusive, then P( A B ) = 0. Therefore, two mutually exclusive events cannot be independent, unless at least one of them has probability 0. 1. The probability that a randomly selected student at Anytown College owns a bicycle is 0.55, the probability that a student owns a car is 0.30, and the probability that a student owns both is 0.10. Are events {a student owns a bicycle} and {a student owns a car} independent? P( B C ) P( B ) × P( C ). 0.10 0.55 × 0.30. B and C are NOT independent . 1 ½ . During the first week of the semester, 80% of customers at a local convenience store bought either beer or potato chips (or both). 60% bought potato chips. 30% of the customers bought both beer and potato chips. Are events {a randomly selected customer bought potato chips} and {a randomly selected customer bought beer} independent? [ Recall that P(Beer) = 0.50. ] P( B PC ) = P( B ) × P( PC ). 0.30 = 0.50 × 0.60. B and PC are independent .

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Events A, B and C are independent if and only if P ( A B ) = P ( A ) P ( B ) , P ( A C ) = P ( A ) P ( C ) , P ( B C ) = P ( B ) P ( C ) , and P ( A B C ) = P ( A ) P ( B ) P ( C ) 1 ¾ . Suppose that a fair coin is tossed twice. Consider A = {H on the first toss}, B = {H on the second toss} and C = {exactly one H in two tosses}. S = { TT, TH, HT, HH }, A = { HT, HH }, B = { TH, HH }, C = { TH, HT }. P( A ) = 1 / 2 , P( B ) = 1 / 2 , P( C ) = 1 / 2 . a) Are A and B independent?
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