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\title{Stat 185 - In class problems \\
\large Wednesday, October 4}
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\noindent Our quiz on Friday will look quite a lot like this!

\begin{enumerate}
	\item 
	\begin{enumerate}
		\item Suppose I roll one fair, six-sided die. \\ What  is the probability that I roll a 2 or a 3?
		\item Suppose I roll two fair, six-sided die. \\ What  is the probability that I roll a 2 and a 3?
		\item What is the distinction between parts (a) and (b)?
	\end{enumerate}
	
	\item Suppose I can by a lottery ticket for \$1 to get 1 chance in $10,000$ to win $\$10,000$ and 99 chances in $10,000$ 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 & 4 & 8 \\
    		\hline
            $P(X)$ & 0.2 & 0.3 & 0.1 & 0.4
        \end{tabular}
        \end{center}
        
        \begin{enumerate}
        		\item Write down the specific formula showing that $E(X) = 4$.
		\item Write down the specific formula to evaluate $\sigma(X)$.
        \end{enumerate}
        
        \item According to the UNCA Factbook, 666 students enrolled as Freshmen and 303 students enrolled as transfer students in the Fall of 2016. If we randomly select 10 of
        those new students, what is the probability that exactly 3 or 4 of them will be transfer students?

\end{enumerate}




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