Final answer:
To find the probability of having a certain number of men in the subcommittee, we can use the hypergeometric distribution. The formula involves calculating the number of ways to choose men and women from the total population and the total number of ways to choose the subcommittee members.
Step-by-step explanation:
In this problem, we have a committee consisting of 39 members, with 21 men and 18 women. A subcommittee of 13 members will be randomly selected from the committee. To find the probability of having a certain number of men on the subcommittee, we can use the hypergeometric distribution.
The hypergeometric distribution is used when we are sampling without replacement from two groups, in this case, men and women. The probability of selecting a certain number of men from the 13-member subcommittee can be calculated using the formula:
Find the number of ways to choose k men from the 21 men.
Find the number of ways to choose (13-k) women from the 18 women.
Find the number of ways to choose 13 members from the total 39 members.
Calculate the probability by dividing the product of the above three values by the total number of ways to choose 13 members from 39.
For example, to find the probability of having at least 9 men on the subcommittee, we need to calculate the probability of having 9, 10, 11, 12, or 13 men on the subcommittee and sum up the individual probabilities.