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 three 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?

Answer 1

Answer:

(a) The probability that all members of the committee are men is 0.3818.

(b) The probability that at least 1 member of the committee is a woman is 0.6182.

Step-by-step explanation:

The number of men in the board of directors is 9.

The number of women in the board of directors is 3.

A committee of three is randomly selected from the board.

(a)

Compute the probability that all members of the committee are men as follows:

P (Selecting 3 men) = n (Selecting 3 men) ÷ n (Selecting 3 members)

                                 $=\frac{{9\choose 3}}{{12\choose 3}}\\= \frac{84}{220} \\=0.3818$

Thus, the probability that all members of the committee are men is 0.3818.

(b)

Compute the probability that at least 1 member of the committee is a woman as follows:

P (At least 1 woman) = 1 - P (All 3 men)

                                 $=1-0.3818\\=0.6182$

Thus, the probability that at least 1 member of the committee is a woman is 0.6182.