Question

At a casino, there is a game where you draw a card from a standard deck of 52 cards. If you get a black card, you win nothing. If you get a heart, you win $5. If you get a diamond, you win $10. There is an additional $20 bonus for the King of diamonds.
a) Create a PDF for a variable X, which represents the amount of money you can win by playing this game.
b) What is the expected amount you’ll win from this game?
c) Would a risk-neutral player pay $5 for a chance to play this game?

Answer 1

X represents the amount of money win playing the game.

X can take the value 0 if the card is black with probability 26/52 since there are 26 black cards

X can take the value 5 if the card is heart with probability 13/52 since 13 cards are heart

X can take the value 10 if the card is diamond and not a king with probability 12/52 (12 diamond cards are there excluding king)

X can take the value 30(10 for diamond+ 20 for diamond king) with probability 1/52

a) Hence the pdf is given by

X: 0 5 10 30

P(X): 26/52 13/52 12/52 1/52

b) The expected amount of money=E(X)=0x(26/52)+5x(13/52)+10x(12/52)+30x(1/52)=215/52=4.13

d)A risk neutral player won't invest $5 since the expected return is 4.13