quiz-1_sol

quiz-1_sol - AMS-131: Introduction to Probability Theory...

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AMS-131: Introduction to Probability Theory (Spring 2008) Quiz 1 Solutions 1. (6 points). Assume that the probability that student A will fail a certain mathematics examina- tion is 0 . 5; the probability that student B will fail the same examination is 0 . 2; and the probability that both student A and B will fail the examination is 0 . 1. (a) What is the probability that neither student A nor student B will fail the examination? Solution: Let A and B be the events that student A and B , respectively, will fail the examination. It is given that Pr( A ) = 0 . 5; Pr( B ) = 0 . 2; and Pr( A B ) = 0 . 1. The event that “neither student A nor student B will fail the examination” can be expressed as A c B c ; its probability can be computed as follows, Pr( A c B c ) = Pr { ( A B ) c } = 1 - Pr( A B ) = 1 - (Pr( A ) + Pr( B ) - Pr( A B )) = 1 - (0 . 5 + 0 . 2 - 0 . 1) = 0 . 4. (b) What is the probability that exactly one of the two students will fail the examination?
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