SOLUTION: Mark draws one card from a standard deck of 52. He receives $0.50 for a heart and $0.70 for an ace, but $0.75 for the ace of hearts. How much could he pay to play this game per dra

Algebra ->  Statistics  -> Central-limit-theorem -> SOLUTION: Mark draws one card from a standard deck of 52. He receives $0.50 for a heart and $0.70 for an ace, but $0.75 for the ace of hearts. How much could he pay to play this game per dra      Log On


   

Question 1128750: Mark draws one card from a standard deck of 52. He receives $0.50 for a heart and $0.70 for an ace, but $0.75 for the ace of hearts. How much could he pay to play this game per draw if he expects to break even in the long run?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


His expected payouts and the corresponding probabilities are

$0.75 * (1/52) for the ace of hearts
$0.70 * (3/52) for any of the other aces
$0.50 * (12/52) for any of the other hearts
$0.00 * 36/52) for any of the other cards

His total expected payout is

.75%281%2F52%29%2B.70%283%2F52%29%2B.50%2812%2F52%29+=+8.85%2F52 = 17.01923 to 5 decimal places.

So he can't realistically expect to EXACTLY break even. If he pays $0.17 to play the game, then in the long run he can expect to come out very slightly ahead.