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
To calculate the expected profit per customer, we can subtract the expected payoff from the cost per play.
First, let's calculate the expected payoff. The probability of drawing an ace from a deck of 52 cards is 4/52, as there are 4 aces in a standard deck. The payoff for drawing an ace is $4.
Expected payoff = (Probability of drawing an ace) * (Payoff)
= (4/52) * $4
= $0.3077
Now, we can calculate the expected profit per customer by subtracting the expected payoff from the cost per play:
Expected profit per customer = Cost per play - Expected payoff
= $0.50 - $0.3077
= $0.1923
Therefore, the expected profit per customer is $0.1923.