From a group of 3 men and 4 women, a delegation of 2 is selected. let x be the random variable that represents the number of women selected. write the probability distribution and find the expected number of women in the delegation?

Let random variable x be the delegated number of men.

x values are 0, 1, 2, 3

The corresponding probabilities are:

P (x=0) = 3C2/7C2=3/21

P (X=1) = 3C1*4C1/7C2=12/21

P (X=2) = 3C2/7C2=3/21

P (X=3) = 3C2/7C2=3/21

Hence the expected value will be:

E (x) = [0*3+1*12+2*3+3*3]/21

E (x) = 27/21=1.29