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

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}$