Start by defining a random variable. Let X be the random variablenumber of diamonds in the hand.

Calculate Pr(X = 0), Pr(X = 1), Pr(X = 2) and Pr(X = 3).

Let Y be the random variableamount of money ($) player wins.

State the value of Pr(Y = 0), Pr(Y = 20), Pr(Y = 40) and Pr(Y = 60).

Let m be the amount of money ($) paid to play the game.

For a fair game, E(Y) = m. Therefore:

m = Pr(Y = 0) (0) + Pr(Y = 20) (20) + Pr(Y = 40) )40 + Pr(Y = 60) (60) = ....