Chapter 16, Problem 3E

(a)

To determine

To find: the probability model for the amount that win.

Explanation of Solution

Probability model for the amount that win is

$X$	$0	$5	$10	$20
$P\left(X=x\right)$	$\frac{26}{52}$	$\frac{13}{52}$	$\frac{13}{52}$	$\frac{1}{52}$

(b)

To determine

To find: the expected amount for the win.

Answer to Problem 3E

$4.13

Explanation of Solution

The expected value of X is given by,

  $\begin{array}{c}E\left(X\right)={\displaystyle \sum xP\left(x\right)}\\ =0\left(\frac{26}{52}\right)+5\left(\frac{13}{52}\right)+10\left(\frac{12}{52}\right)+30\left(\frac{1}{52}\right)\\ =\frac{65}{52}+\frac{120}{52}+\frac{30}{52}\\ =\$4.13\end{array}$

Expected amount for win is $4.13

(c)

To determine

To find: that would be willing to pay to play this game.

Explanation of Solution

There would be willing to pay amount less than $4.13, although that is expected amount and it will strike even or make profit.