Chapter 12, Problem AP4.32CPT

To determine

To find out which of the two wagers should you prefer.

Answer to Problem AP4.32CPT

Option (a) is the correct option.

Explanation of Solution

In the question, we are offered a choice of the following stages mentioned in the question. If we draw an ace then we win $\$10$ otherwise lose $\$1$ and in the second if we draw a heart then we win $\$2$ otherwise lose $\$1$ . The expected value is the sum of the product of each possibility with its probability are:

Wager $1$ :

  $\begin{array}{l}E(X)={\displaystyle \sum xP(x)}\\ =\$10\times \frac{4}{52}+(-\$1)\times \frac{48}{52}\\ =-\$0.15\end{array}$

Wager $2$ :

  $\begin{array}{l}E(X)={\displaystyle \sum xP(x)}\\ =\$2\times \frac{13}{52}+(-\$1)\times \frac{39}{52}\\ =-\$0.25\end{array}$

Thus, we conclude that wager $1$ is preferred because the expected value is higher and thus you will be more likely to make a profit with wager $1$ . Thus, option (a) is the correct option.