A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The gamecosts $6 to play, and you win if the number you bet appears on any of the dice. The distribution for theoutcomes of the game (including the profit) is shown below: $$\begin{array} { c c c }
\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability of Observing } \
\hline 0 & - \$ 6 & 125 / 216 \
1 & \$ 6 & 75 / 216 \
2 & \$ 8 & 15 / 216 \
3 & \$ 18 & 1 / 216 \
\hline
\end{array}$$ Find your expected profit from playing this game.
A) -$0.77
B) $0.50
C) $6.18
D) $3.39

Question

A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The gamecosts $6 to play, and you win if the number you bet appears on any of the dice. The distribution for theoutcomes of the game (including the profit) is shown below: $$\begin{array} { c c c } 
\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability of Observing } \
\hline 0 & - \$ 6 & 125 / 216 \
1 & \$ 6 & 75 / 216 \
2 & \$ 8 & 15 / 216 \
3 & \$ 18 & 1 / 216 \
\hline
\end{array}$$ Find your expected profit from playing this game.
A) -$0.77
B) $0.50
C) $6.18
D) $3.39

Quizplus · Accepted Answer

The expected profit is calculated by multiplying each profit by its probability and summing these products: $(-6 \times \frac{125}{216}) + (6 \times \frac{75}{216}) + (18 \times \frac{1}{216}) + (8 \times \frac{15}{216}) = -0.77$.

A Dice Game Involves Throwing Three Dice and Betting on One