Chapter 6.1, Problem 29E

To determine

To find: The mean amount that would be won.

Answer to Problem 29E

The required amount is -$0.15.

Explanation of Solution

Given:

The wining amount is $10.

Loss amount is $-1

Calculation:

The probability of wining and losing can be calculated as:

  $\begin{array}{c}P\left(Win\right)=\frac{\text{Number of aces}}{\text{Total cards}}\\ =\frac{4}{52}\\ =\frac{1}{13}\end{array}$

Similarly,

  $\begin{array}{c}P\left(Loss\right)=1-P\left(Win\right)\\ =1-\frac{1}{13}\\ =\frac{12}{13}\end{array}$

The expected amount is calculated as:

  $\begin{array}{c}E\left(X\right)=10\times \frac{1}{13}+\left(-1\right)\times \frac{12}{13}\\ =-0.15\end{array}$

Thus, the required mean amount is $-\$0.15$ .

Hence, the correct option is (c).