Question

Certify Completion Icon Tries remaining:3 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 $296. Otherwise, you have to pay your friend $17. 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 bet is –$0.95.

Step-by-step explanation:

Number of cards in a standard deck = 52

Number of diamonds in a standard deck = 13

The probability (P) that the two cards that will be drawn without replacement will be diamonds is therefore as follows:

P = (13 / 52) * (12 / 51) = 0.0588

The probability (P) that the two cards that will be drawn without replacement will NOT be diamonds is also as follows:

1 – P = 1 – 0.0588

1 – P = 0.9412

Amount your friend will pay you if both cards are diamonds = $296

Amount you will pay your friend if both cards are NOT diamonds = -$17 (Note that this is negative since it is a loss)

Expected value of the bet = (P * $296) + ((1 – P) * ($-17)) = (0.0588 * $256) – (0.9412 * 17) = –$0.95