Question

From a group of 6 women and 3 men, a delegation of 3 is selected. Find the expected number of women in the delegation. What is the expected number of women? (Round to two decimal places as needed.)

Answer 1

It is given that there is a group of 6 women and 3 men. A delegation of 3 is selected out of 9. The number of ways of selecting 3 out of 9 people is There are four cases. Let X be the number of women selected. When X is equal to 0, that is, no women is selected the probability corresponding to X=0 is given as follows: When X is equal to 1, that is, one women is selected, the probability corresponding to X= 1 is given as follows: When X is equal to 2, that is, two women are selected, the probability corresponding to X=2 is given as follows: When X is equal to 3, that is, three women are selected, the probability corresponding to X= 3 is given as follows:

The probability table is given as follows: x P(X=x) The expected number of women in the delegation is given as follows: E(X)= xp(x) -2 Therefore, the expected number of women in the delegation is 2.