A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $11 to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below: 0 -$11 125/216 $$\begin{array} { c c c }
\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability } \
\hline 0 & - \$ 11 & 125 / 216 \
1 & \$ 11 & 75 / 216 \
2 & \$ 13 & 15 / 216 \
3 & \$ 33 & 1 / 216 \
\hline
\end{array}$$ Find your expected profit from playing this game.
A) -$1.53
B) $0.50
C) $11.20
D) $5.96

Question

A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $11 to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below: 0 -$11 125/216 $$\begin{array} { c c c } 
\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability } \
\hline 0 & - \$ 11 & 125 / 216 \
1 & \$ 11 & 75 / 216 \
2 & \$ 13 & 15 / 216 \
3 & \$ 33 & 1 / 216 \
\hline
\end{array}$$ Find your expected profit from playing this game.
A) -$1.53
B) $0.50
C) $11.20
D) $5.96

Quizplus · Accepted Answer

The expected profit is calculated by multiplying each profit by its probability and summing the results: (-$11 * 125/216) + ($11 * 75/216) + ($13 * 15/216) + ($33 * 1/216) = -$1.53.

A Dice Game Involves Rolling Three Dice and Betting on One