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homework_2_ans

# homework_2_ans - St Johns University Department of...

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St. John’s University 03/23/08 Department of Mathematics and Computer Science Course MTH 1210 Homework #2 (answers) PROBLEMS INVOLVING CONDITIONAL PROBABILITY #1. Women Joggers . In a certain area, 15% of the population are joggers and 40% of the joggers are women. If 55% of those who do not jog are women, find the probabilities that an individual from that community fits the following descriptions. ( a) A woman jogger ( b ) Not a jogger ( c ) A woman Event A : an individual is a jogger; P(A) = 0.15 Event Ā : an individual is not a jogger (the event Ā is complementary to A ). Event B : an individual is a woman . Event B|A : an individual is a woman, given an individual is a jogger; P(B|A) = 0.4 . Event B|Ā : an individual is a woman, given an individual is not a jogger; P(B|Ā) = 0.55 . (a) A woman jogger : P(B∩A) = P(A∩B) = P(A)*P(B|A) = 0.15*0.4 = .06 [see (5.4a,b)] (b) an individual is not a jogger: P(Ā) = 1 – P(A) = .85 (c) A woman: P(B) = P(B∩A) + P(B∩Ā) [see (5.6)] P(B∩Ā) = P(Ā)*P(B|Ā) = 0.85*0.55 = 0.4675 Thus, P(B) = P(B∩A) + P(B∩Ā) = 0.06 + 0.4675 = 0.5275 #2. Color blindness . The table below shows relative frequencies for

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