Question

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.

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.