A delegation of 3 is selected from a city council made up of 3 liberals and 5 conservatives. What is the expected number of liberals in the​ delegation?

Question

A delegation of 3 is selected from a city council made up of

3

liberals and

5

conservatives. What is the expected number of liberals in the​ delegation?

Answer 1

A delegation of 3 is selected from a city council made up of 3 liberals and 5 conservatives. What is the expected number of liberals in the​ delegation?

Step-1

Given

Delegation size = 3

No. of liberals = 3

No. of conservatives = 5

Step-2: Get combinations of probabilities in the delegation

P( 0 liberals, 3 conservatives) = ((3 choose 0)*(5 choose 3))/ (8 choose 3) = (1*10)/56 = 0.179

P( 1 liberals, 2 conservatives) = ((3 choose 1)*(5 choose 2))/ (8 choose 3) = (3*10)/56 = 0.536

P( 2 liberals, 1 conservatives) = ((3 choose 2)*(5 choose 1))/ (8 choose 3) = (3*5)/56 = 0.268

P( 3 liberals, 0 conservatives) = ((3 choose 3)*(5 choose 0))/ (8 choose 3) = (1*1)/56 = 0.0179

Step-3: Compute weighted sum of individual probabilities

Answer: Expected number of liberals in the​ delegation

= 0*0.179 + 1*0.536 + 2*0.268 + 3*0.0179 = 1.2757