In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 11. The probability that you win is $\frac { 1 } { 18 }$ , and if you win, your profit is $15.
If you lose, you lose $1. What is the expected value of your profit?
A) $0.83
B) -$0.94
C) -$0.11
D) $0.11

Question

Quizplus · Accepted Answer

We can calculate the expected value of the profit as:
\begin{align*}
E(	ext{profit}) &= P(	ext{win})	imes (	ext{profit if win}) + P(	ext{lose})	imes (	ext{profit if lose}) \
&= \frac{1}{18}	imes 15 - \frac{17}{18}	imes 1 \
&= \frac{5}{6}	imes \frac{1}{18} - \frac{17}{18} \
&= -\frac{1}{6} \approx -0.1667
\end{align*}
So the expected value of the profit is a loss of approximately $0.17. Therefore, the best choice is not to play this bet.

In the Game of Craps, Two Dice Are Rolled, and People