A Dice Game Involves Throwing Three Dice and Betting on One

Multiple Choice

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