An urn contains three red balls five white balls and two bla

An urn contains three red balls, five white balls, and two black balls. Three balls are drawn from the urn at random without replacement. For each red ball drawn, you win $6, and for each black ball drawn, you lose $9. Let X represent your net winnings.

Compute E(X), your expected net winnings.

E(X) =

Solution

P(Red) = 3 / (3+5+2) = 3 / 10
P(White) = 5/ (3+5+2) = 5/10
P(Black) = 2 / (3+5+2) = 2/10

E(X) = 6 * 3/10 + 0 * 5/10 - 9 * 2/10 = 18/10 - 18/10 = 0