Question

You pay $20 to play a game. You choose a card from a standard deck of cards plus two jokers (total of 54 cards) at random. If you pick a joker you get $200; if you pick an ace you get $50; if you get a face card you get $25. Otherwise you receive nothing. Calculate the expected value of this game.

Answer 1

Probability of getting a joker = 2/54 = 1/27 Net Gain = 200 - 20 = 180

Probability of getting an ace = 4/54 = 2/27. Net gain = 50 - 20 = 30

Probability of getting a face card = 12/54 = 6/27. Net Gain = 25 - 20 = 5

Probability of getting Nothing = 1 - [1/27 + 2/27 6/27] = 1 - 9/27 = 18/27. Net Gain = -20

Therefore Expected Value = SUM(Gain * probability) = (180 * 1/27) + (30 * 2/27) + (5 * 6/27) + (-20 * 18/27)

= 180/27 + 60/27 + 30/27 - 360/27

= -90 / 270

= -0.33 dollars