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
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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.