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?



The probability of drawing an ace is 4/52 or 1/13
The expected payout is 4.00*1/13=.30769
The income is 0.50
so the expected profit is .50-.30769
=.1923
or 19 cents.

Suppose you have 104 people playing.
So the game takes in $52
There is a probability that 1/13 of 104 will win, which is 8
so the payout is $32
for a profit of $20, but there were 104 people playing, so the profit per person is 20/104 or .1923
(notice it makes no difference how many people play)

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