1. ## Card Problem

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? 2. Originally Posted by zackgilbey 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) = ....

3. that makes it easier, but what do they mean by 'fair'?

4. Originally Posted by zackgilbey
that makes it easier, but what do they mean by 'fair'?
Fair means that the E(amount won) = amount paid to play, that is, E(Y) = m, that is, E(profit) = 0.