A 3 person committee, possibly more, is to be formed from a set of 5 men and 3 w

Question

A 3 person committee, possibly more, is to be formed from a set of 5 men and 3 women. Selection is random, but it is required that the committee must have at least one man and at least one woman. The procedure used is to first select 3 people, and if the gender requirement is met, selection ends there. If not, then people are added to the committee one at a time from those remaining until the requirement is met. Existing members are not dropped.

1.Find the probability that selection ends with the first 3 people chosen.

2.Suppose we know that the committee consisted of 4 people in the end. Find the probability that the last person chosen was a woman.

Explanation / Answer

1) probability of selecting 1 member as man 5/8 and probability of selecting second member as woman 3/7

or probability of selecting 1 member as woman 3/8 and probability of selecting second member as man 5/7

Required probability = 5/8 * 3/7 + 3/8 * 5/7

= 30/56

2) In this case first 3 people selected are men .hence, to complete the committee 1 woman is required

1 woman from 3 can be selected in 3C1 ways

Required probability = 3C1 / 5C1

= 3/5

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