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) $\$ 3.90$

Question

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) $\$ 3.90$

Quizplus · Accepted Answer

The expected profit is calculated by multiplying each profit by its corresponding probability and summing these products: $(-7) \times (125/216) + 7 \times (75/216) + 9 \times (15/216) + 21 \times (1/216) = - \$ 0.92$.