Two student council representatives are chosen at random fro

Two student council representatives are chosen at random from a group of 7 girls and 3 boys. Let G denote the distribution over the number of girls chosen.

a What is the expectation of G?

Solution

G = distribution over the number of girls chosen

so, G = 0 (means 0 girls are selected as representative) with prob. ( 3 /10) * ( 2/9) = 0.066..
   =1 ( means 1 girl is selected) with prob. = ( 7/10)*(3/9) + ( 3/10)*( 7/9) = 0.467..
   =2 ( means 2 girls are selected) with prob. = ( 7/10) * ( 6/9) = 0.467...
Expectation = 0*(0.066) + 1*( 0.467) + 2*( 0.467) = 1.4.....