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:

Archangel Michael

One of the principal angels in Christian and Jewish tradition, often depicted as a protector and leader of the army of God against the forces of evil.

Early Byzantine

Referring to the initial period of the Byzantine Empire, characterized by the spread of Christianity and the establishment of its unique art and architectural styles.

Ivory Diptych

Two panels, often intricately carved from ivory and hinged together, historically used for religious and ceremonial purposes.

Ascension Scene

Refers to the depiction in art of the biblical event where Jesus Christ ascends to heaven in the presence of his apostles.