Question

A committee of 6 people is to be chosen from a group of 5 men and 7 women. What is the probability that the committee will consist of 4 men and 2 women? (Round to four decimal places)

A.0.0789
B.0.1136
C.0.1944
D.O .2045

Answer 1

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.