Final answer:
The probability of selecting 4 men and 2 women from a group of 5 men and 7 women is approximately 0.2045.
Step-by-step explanation:
The probability that the committee will consist of 4 men and 2 women can be calculated using the hypergeometric probability formula. The formula is:
P(x) = (C(r, x) * C(b, n-x)) / C(r+b, n)
where:
P(x) is the probability of getting x men,
C(r, x) is the number of ways to choose x men from the total number of men,
C(b, n-x) is the number of ways to choose (n-x) women from the total number of women,
C(r+b, n) is the total number of ways to choose a committee of size n from the total number of people.
Substituting the given values into the formula, we have:
P(4 men and 2 women) = (C(5, 4) * C(7, 2)) / C(12, 6)
Calculating this expression gives the answer to be approximately 0.2045, which is option D.