Question

Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards without replacing the first card, you give him $40. Otherwise, he pays you $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.

Answer 1

Given:

The total number of face cards is 12.

The total number of cards is 52.

The probability of 2 successive face cards is,

`\begin{gathered} (12*11)/(52*51)=(11)/(13*17) \\ =(11)/(221) \end{gathered}`

The probability of not getting 2 face cards is,

`\begin{gathered} P(\bar{E})=1-P(E) \\ =1-(11)/(221) \\ =(210)/(221) \end{gathered}`

Next, to find the expected value.

`\begin{gathered} (11)/(221)*(-40)+(210)/(221)(10)=-(440)/(221)+(2100)/(221) \\ =\text{ \$}7.51 \end{gathered}`

Hence, the expected value of the bet is $7.51.