Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three non-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 give him $10. Otherwise, he pays you $20. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

Question

Maximilian Bennett

Mathematics

28 March, 15:12

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three non-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 give him $10. Otherwise, he pays you $20. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

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Rocco · Answer 1

First let us calculate the probability that three non-face cards will be drawn in succession without replacement.

There are 40 non-face cards in a deck of 52 cards.

Probability of 3 successive non-face cards = (40/52) * (39/51) * (38/50) = 0.447

Therefore, the probability that it will not be 3 successive non-face cards is 1-0.447 = 0.553

Hence, for each game the expected return would be:

Return = 0.447 * (-$10) + 0.553 ($20) = $6.59 per bet

For 25 bets:

Total return = $6.59 * 25

Total return = $164.75

If the bet is performed 25 times, expect to win $164.75.