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 diamonds, your friend will pay you $37. Otherwise, you have to pay your friend $5.

Step 1. What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.

Step 2. If this same bet is made 713 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

Step 1: Expected value = -2.53 dollars

He makes - 1,803.89 dollars over 713 of these bets.

Step 2:

Explanation:

Expected value of bet = (Winning probability * winning amount) - (losing probability * losing amount)

Winning probability = (13/52) * (12/51) = 0.0588

Losing probability = 1 - 0.0588 = 0.9412

Expected value = (37 * 0.0588) - (5 * 0.9412)

Expected value = -2.53 dollars

If this same bet of expected value -2.53 dollars is made 713 times, our expected losses are:

2.53 * 713 = 1,803.89 dollars

Thus he makes - 1,803.89 dollars over 713 of these bets.