In a particular game of chance, a 3-card hand is dealt to the player from a standard deck of 52 cards. The player wins $20 for each diamond in their hand. If the game is fair, how much should the player have to pay to play this game?
Start by defining a random variable. Let X be the random variable number of diamonds in the hand.
Calculate Pr(X = 0), Pr(X = 1), Pr(X = 2) and Pr(X = 3).
Let Y be the random variable amount of money ($) 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) = ....