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.

Question

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
(click or scroll down)

👇

Answer 1

Bot GPT 3.5 answered
22 days ago

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.