The Lottery Commission Has Designed a New Instant Lottery Game $$\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}$$

question 11

Short Answer

The lottery commission has designed a new instant lottery game. Players pay $1.00 to scratch a ticket, where the prize won, X, (measured in $) has the following discrete probability distribution : $$\begin{array} { | c | c | } \hline X & P [ X ] \\\hline 0 & 0.95 \\\hline 10 & 0.049 \\\hline 100 & 0.001 \\\hline\end{array}$$ Which of the following best describes the expected value of X ? $\begin{array}{|l|l|}\hline A&\text {In the long run, the average prize won per \( \$ 1 \) played is \( \$ 0 \). }\\\hline B&\text {In the long run, the average prize won per \( \$ 1 \) played is \( \$ 0.41 \). }\\\hline C&\text { In the long tun, the average prize won per \( \$ 1 \) played is \( \$ 0.59 \).}\\\hline D&\text {None of these choices are correct }\\\hline \end{array}$

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Definitions:

Total Revenue

The overall amount of income generated by a business from its activities, such as sales of goods or services, before deducting expenses.

Total Variable Cost

The sum of all costs that vary directly with the level of production or output, such as raw materials and direct labor expenses.

Operating Leverage

A measure of how revenue growth translates into growth in operating income due to fixed versus variable costs.

Profit And Loss Statement

A financial statement that summarizes the revenues, costs, and expenses incurred during a specific period, reflecting the company's profit or loss.