A committee of 3 members is selected from a club made up of

A committee of 3 members is selected from a club made up of 9 junior members and 21 senior members. What is the expected number of juniors in the committee? What is the expected number of juniors? (Round your answer to the nearest hundredth, if necessary.)

Solution

x: 0 1 2 3
P(x):

P(x = 0) = 21c3/30c3 = 19/58
P(x = 1) = 9c1*21c2/30c3 = 27/58
P(x = 2) = 9c2*21c1/30c3 = 27/145
P(x = 3) = 9c3*21c0/30c3 = 3/145

E(x) = 0*(19/58)+ 1*(27/58)+2*(27/145)+ 3*(3/145)
= 0.9