Question
From a group of 7 men and 4 women, a committee of 4
persons is to be formed. The probability that the committee has at least one woman is:Solution
Total people = 7 men + 4 women = 11 Total ways to form a committee of 4 = C(11, 4) We are asked to find the probability that the committee has at least one woman. This is equal to: 1 – (Probability that all 4 are men) Number of ways to choose 4 men from 7 = C(7, 4) So, Required probability = 1 – [C(7, 4) / C(11, 4)] = 1 – [35 / 330] = 1 – (7 / 66) = 59 / 66
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