A standard deck of cards contains 52 cards, of which 4 are aces. You are offered the following wager: draw one card at random from the deck. You win $10 if the card drawn is an ace. Otherwise, you lose $1. If you make this wager very many times, what will be the mean outcome?
A) about -$1, because you will lose most of the time
B) about $9, because you win $10 but lose only $1
C) about -$0.15, that is, on the average you lose about 15 cents per play
D) about $0.77, that is, on the average you win about 77 cents per play
E) about $0, because the random draw gives you a fair bet

Question

Quizplus · Accepted Answer

The mean outcome is calculated by multiplying the probability of each outcome by its value and summing these products. With 4 aces in a 52-card deck, the probability of drawing an ace is 4/52 (or 1/13), and the probability of not drawing an ace is 48/52 (or 12/13). The expected value is (1/13)*$10 + (12/13)*(-$1) = $10/13 - $12/13 = -$2/13, which is approximately -$0.15.

A Standard Deck of Cards Contains 52 Cards, of Which