Two balls are chosen randomly from an urn containing 8 yello

Two balls are chosen randomly from an urn containing 8 yellow, 4 black, and 2 red balls. Let Y represent the number of black balls chosen. The discrete probability distribution is shown below.

(Y=0) = 45/91
P(Y=1) = 40/91
P(Y=2) = 6/91

What is the mean, or expected value, of Y?

With the situation described above, now suppose that you win $2 for each black ball, and nothing for any other color. What is the expected value of your winnings?

Solution

a.) E(Y) = Sum of y*P(y) = (0)*(45/91) + (1)*(40/91) + (2)*(6/91) = 4/7

b.) Expected value of winnings = $2*(4/7) = $8/7 = $1.143