Question

At a fair run by a local charity organization, it costs 50 cents to try one's luck in drawing an ace from a deck of 52 playing cards. What is the expected profit per customer if they pay $4 if and only if a person draws an ace.

I presume that the drawn card is replaced after every play. First calculate the expected payoff -- the probability of hitting the payoff times the payoff - or (4/52)*$4. = 0.3077 So, the expected profit per play is $0.50 less $0.3077