Question

There are 15 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 6 females?

Answer 1

The probability of selecting exactly 6 females in a committee of 11 members can be calculated using the hypergeometric distribution formula.

Step-by-step explanation:

To find the probability of exactly 6 females in a randomly chosen committee of 11 members, we can use the hypergeometric distribution.

In this case, we have a population of 15 females and 12 males, and we want to choose 6 females and 5 males for our committee.

The total number of ways to choose 6 females out of 15 is C(15,6) and the total number of ways to choose 5 males out of 12 is C(12,5). The total number of ways to choose 11 members out of 27 (15 females + 12 males) is C(27,11).

Therefore, the probability of exactly 6 females in the committee is:

P(6 females) = (C(15,6) * C(12,5)) / C(27,11) = (5005 * 792) / 547575 = 0.7219