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 hearts, your friend will pay you $606$ 606. Otherwise, you have to pay your friend $36$ 36. Step 1 of 2 : What is the expected value of your bet? Round your answer to two decimal places. Losses must be expressed as negative values.

Answer 1

The expected value of the wager is $1.77

Explanation:

Firstly, we need to calculate the probability that both are hearts

In a standard deck of cards, we have 13 cards in the heart suite

Thus the probability that both cards are hearts without replacement = 13/52 * 12/51 = 1/17

Now the probability that at least one is a heart = 1 - probability that both are hearts = 1 -1/17 = 16/17

Thus, the expected value of the wager = 606(1/17) - 36(16/17) = 35.65-33.88 = $1.77

The expected value of the wager = $1.77