Suppose that you and a friend are playing cards and decide to make a bet. If you draw three face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacement, you win $40. Otherwise, you pay your friend $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

1 answer

To find the expected value of the bet, we first need to find the probability of drawing three face cards in succession.

There are 12 face cards in a standard deck of 52 cards. After drawing one face card, there are 11 face cards left in a deck of 51 cards. After drawing the second face card, there are 10 face cards left in a deck of 50 cards.

Therefore, the probability of drawing three face cards in succession is (12/52) * (11/51) * (10/50) = 0.01294.

Now we can calculate the expected value of the bet:
(0.01294 * $40) - (0.98706 * $10) = $0.52

Therefore, the expected value of the bet is $0.52.