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\title{Stat 185 -  Quiz3 \\
\large Friday, October 6}
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Name:\underline{\hspace{2.2in}}
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\noindent Please write complete solutions (answers with supporting work) to these problems separate paper.

\begin{enumerate}
	\item I've got a twelve sided die with six sides labeled 1, four sides labeled 2, and two sides labeled 3.
	\begin{enumerate}
		\item Suppose I roll that die once. \\ What  is the probability that I roll a 2 or a 3?
		\item Suppose I roll twice. \\ What  is the probability that I roll a 2 and a 3?
	\end{enumerate}
	
	\item Suppose I can buy a lottery ticket for \$1 to get 1 chance in $100,000$ to win $\$10,000$ and 1 chance in $1,000$ to win $\$100$.
	What is the expected value of that ticket?
	
	\item Consider a random variable $X$ with the following distribution:
	
	\begin{center}
        \begin{tabular}{c||c|c|c|c}
            $X$ & 1 & 2 & 3 & 6 \\
    		\hline
            $P(X)$ & 0.3 & 0.3 & 0.1 & 0.3
        \end{tabular}
        \end{center}
        
        \begin{enumerate}
        		\item Write down the specific formula showing that $E(X) = 3$.
		\item Write down the specific formula to evaluate $\sigma(X)$.
        \end{enumerate}
        
        \item According to last year's UNCA Factbook, there were 823 Faculty and Staff employed at UNCA and 3727 students enrolled.
		Suppose we randomly choose pick 20 people from this population of 4550 people. What is the probability that exactly 16 of
		those people are students? Be sure to express your answer as a formula.
\end{enumerate}




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