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.

Question

Humberto

Mathematics

4 October, 13:35

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.

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Answers (1)

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Ronan Kane · Answer 1

The expected value of the wager is $1.77

Step-by-step 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