Question

Consider a game that consists of dealing out two cards from a deck of four cards....

Consider a game that consists of dealing out two cards from a deck of four cards.

The deck contains the Ace of Spades (AS), the Ace of Hearts (AH), the King of Spades (KS) and the 9 of Hearts (9H).

Let X be your total where; aces count as 1 or 11, kings count as 10 and your maximum count is 21 (that is, AA = 12). Also, let A be the number of aces in your hand. Suppose your winnings (Y) are calculated as Y= X - 16- A^4 (A to the power of 4) (a negative value means you lose that amount). Give the probability distribution for your winnings, Y, on a single play of this game.

Math   Statistics-And-Probability   
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Answer #1

There are 6 different pair of cards we can receive. we can enlist all of them separately and calculate the payoffs

Case 1 - getting 2 aces

Y= 12 - 16 - 16 = -20 with probability 1/6

Case 2 - getting AS and KS

Y= 21 - 16 - 1 = 4 with probability 1/6

Case 3 - getting AH and KS

Y= 21 - 16 - 1 = 4 with probability 1/6

Case 4 - getting AS and 9H

Y= 20 - 16 - 1 = 3 with probability 1/6

Case 5 - getting AH and 9H

Y= 21 - 16 - 1 = 3 with probability 1/6

Case 6 - getting KS and 9H

Y = 19 - 16 - 0 = 3 with probability 1/6

The probability distribution of Y is as follows

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