Interpret the Mean of a Discrete Random Variable as an Expected

question 1

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) \(\$ 3.90\)

---

Definitions:

Mathematical Mistakes

Errors made in calculations, often due to incorrect addition, subtraction, multiplication, or division, affecting the accuracy of financial statements.

Material

The quality of information that exists when the omission or misstatement of the information could influence the decision that users make.

Size

in a business or economic context typically relates to the scale or dimensions of a company or market, often measured by metrics such as revenues, employee count, or market share.

Nature

The fundamental qualities or characteristics of something, indicating its intrinsic properties or tendencies.