Question

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards with replacement, you give him $100. Otherwise, he pays you $10. If the same bet was made 20 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.

Answer 1

First, we need to find the probability to get three face cards.

There are 12 face cards:

4 jacks

4 queens

4 kings

= 12 face cards.

There are 52 cards in a deck.

Hence, the probability to get the face cards with replacement is:

`(12)/(52)\cdot(12)/(52)\cdot(12)/(52)=(27)/(1297)`

Let's check the bet:

If he wins:

(27/1297) *(-100)= -2700/2197

other he pays:

(1-27/1297) * (10)= 9.877

The return would be = -2700/2197 + 9.877 = $8.65 per bet

If the bet was made 20 times:

20*$8.65= $173

Answer.

If the bet was made 20 times. He will win $173.