Question

If you draw a card with a value of three or less from a standard deck of cards, I will pay you $41. If not, you pay me $11. (Aces are considered the highest card in the deck). If you played this game 877 times how much would you expect to win or lose?

Answer 1

There are 12 cards with a value ≤ 3 (3 between 1, 2, and 3, and multiply by 4 to count each suit). So the probability of drawing one of these cards and thus winning the game is 12/52 = 3/13.

The expected winnings for playing this game once are

3/13 × ($41) + 10/13 × (-$11) = $1

so after playing 877 times, you can expect to win a total of $877.