Question: Problem 1. A committee will be formed with 4 managers and 3 engineers selected randomly without replacement from 11managers and 19 engineers. What is the

Problem 1. A committee will be formed with 4 managers and 3 engineers selected randomly without replacement from 11managers and 19 engineers. What is the conditional probability that engineer Al is on the committee given that engineer Jane is on the committee? SOLUTION Let A denote that the engineer Al is on the committee, B denote that the engineer Jane is on the committee. One of three vacancies already belongs to Jane, thus Al has 2 opportunities to get one of them. Thus, (17.1) P(ANB) T(19,3) 17 _ PGB C(is,2) 153 - o P(A|B) = Problem 2. In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that four of the tanks contain material in which the viscosity exceeds the customer requirements. (a) What is the probability that exactly one tank in the sample contains high-viscosity material? 24 ! The total number of samples possible is :i =10626. The number of 4 41201 samples in which exactly one tank has high viscosity 1\\(';) (230) = :;I% = 4560. Therefore, the probability 1s: 1360 = 0.43. 10626

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