A card game goes like this: You draw a card from a 52
-card deck. If it is a face card (jack, queen, or king), you win $8
; otherwise, you lose $4
. What is your expected value for this game?
There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a 52-card deck. Therefore, the probability of drawing a face card is 12/52 or 3/13.
The probability of not drawing a face card is 1 - 3/13 = 10/13.
The expected value for this game can be calculated as:
Expected Value = (Probability of Winning) * (Amount Won) - (Probability of Losing) * (Amount Lost)
Expected Value = (3/13) * $8 - (10/13) * $4
Expected Value = $24/13 - $40/13
Expected Value = -$16/13
The expected value for this game is -$16/13, which means on average, you will lose about $1.23 for each play of the game.