Interpret the Mean of a Discrete Random Variable as an Expected

Multiple Choice

Interpret the Mean of a Discrete Random Variable as an Expected Value
-A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The game costs $\$ 7$ 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:
$\begin{array}{ccc}\hline \text { Number of dice with your number } & \text { Profit } & \text { Probability of Observing } \\\hline 0 & -\$ 7 & 125 / 216 \\1 & \$ 7 & 75 / 216 \\2 & \$ 9 & 15 / 216 \\3 & \$ 21 & 1 / 216\end{array}$

Find your expected profit from playing this game.

A) $- \$ 0.92$
B) $\$ 0.50$
C) $\$ 7.18$
D) $\$ 3.90$