A Dice Game Involves Rolling Three Dice and Betting on One

Multiple Choice

A dice game involves rolling three dice and betting on one of the six numbers that are on the dice. The game costs $12 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: $\begin{array}{ccc}\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability } \\\hline 0 & -\$ 12 & 125 / 216 \\1 & \$ 12 & 75 / 216 \\2 & \$ 14 & 15 / 216 \\3 & \$ 36 & 1 / 216 \\\hline\end{array}$

Find your expected profit from playing this game.

A) $\$ 0.50$
B) $\$ 12.20$
C) $- \$ 1.69$
D) $\$ 6.47$