Correct If you draw a card with a value of three or less from a standard deck of cards, I will pay you $\$ 17$. If not, you pay me $\$ 6$. (Aces are considered the highest card in the deck.) Step 2 of 2: If you played this game 745 times how much would you expect to win or lose? Round your answer to two decimal places, Losses must be expressed as negative values. Answer How to enter your answer (opens in new window)

Step 1 ：A standard deck of cards has 52 cards, with 4 cards each of 13 different values (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). Therefore, there are 4 cards each of value 1, 2, and 3, which makes a total of 12 cards with a value of three or less. The probability of drawing one of these cards is therefore \(\frac{12}{52}\).

Step 2 ：If we draw a card with a value of three or less, we win $17. If not, we lose $6. Therefore, the expected value of a single game is \(\left(\frac{12}{52}\right)*17 - \left(\frac{40}{52}\right)*6\).

Step 3 ：To find out how much we would expect to win or lose if we played the game 745 times, we simply multiply the expected value of a single game by 745.

Step 4 ：The expected loss after playing this game 745 times is \(\boxed{-515.77}\) dollars.