You pay .50 cent to draw a card from a deck. if you draw an ace you win ten dollars if you draw a face card(12 in a deck) you win a $1. what is your expected value

The probability that a face card can be drawn from a standard deck of cards is 12/52 which can be simplified into 3/13.

The expected value is the product of the probability and the value.
                       Expected value = (3/13)($1) = $0.23
The difference between the amount spent and the expected value is equal to $0.27.