Suppose we pick 3 students at random from a class with 10 bo

Suppose we pick 3 students at random from a class with 10 boys and 15 girls. Let X be the number of boys selected and Y be the number of girls selected. Find E(X-Y) (Show all work) Hint: answer=-3/5

Solution

P(Boys) = 10/25 = 0.4

P(Girls) = 15/25 = 3/5 = 0.6

E(X) = 3*0.4 = 12/10

E(Y) = 3*0.6 = 1.8 = 18/10

E(X-Y) = E(X) - E(Y) = 12/10 - 18/10 = -6/10 = -3/5