Question

The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly selected from the board to do the writing. a. What is the probability that all members of the committee are men? b. What is the probability that at least 1 member of the committee is a woman?

Solution

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Given: Out of 12 members, 3 are women.

a) P(all three members are men) = (93)/(123)=(987)/(121110)=0.3818{9\choose3}/{12\choose3} = (9*8*7)/(12*11*10) = 0.3818

b) P(at least one member is a woman) = 1 - P(all members are men) = 10.38181=0.618181 - 0.38181 = 0.61818

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