Question

Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are spades, your friend will pay you $225. Otherwise, you have to pay your friend $12. Step 2 of 2 : If this same bet is made 738 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 1

The expected amount you would expect to win or lose after playing the bet 738 times is -$2169.72.

Step-by-step explanation:

To calculate the amount you would expect to win or lose, you need to find the expected value. The expected value is calculated by multiplying the amount you can win by the probability of winning and subtracting the amount you can lose multiplied by the probability of losing.

In this case, the probability of drawing two spades without replacement is (13/52) * (12/51) = 1/17. The amount you can win is $225 and the amount you can lose is $12. Therefore, the expected value is (1/17 * $225) - (16/17 * $12) = -$2.94. Since you play this bet 738 times, you would expect to lose 738 * $2.94 = -$2169.72.