Question

There are 17 female board members and 12 male board members. If a committee of 11 members is randomly chosen, what is the probability that the committee has exactly 4 females?

Answer 1

The probability of having exactly 4 females in a randomly chosen committee of 11 members from 17 females and 12 males is approximately 0.1242.

Step-by-step explanation:

This is a hypergeometric problem because we are choosing the committee from two groups: females (17) and males (12). To calculate the probability of having exactly 4 females in the committee, we need to determine the total number of ways to choose 4 females from 17 females, multiplied by the total number of ways to choose 7 people from the remaining 12 males. Finally, we divide this value by the total number of ways to choose 11 people from a group of 29 (17 females + 12 males).

The probability of having exactly 4 females in the committee is:

P(4 females) = (C(17, 4) * C(12, 7)) / C(29, 11)

P(4 females) ≈ 0.1242