%Caleb McWhorter
%May 6, 2016

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\fancyhead[L]{\Large MAT 221}
\fancyhead[C]{\Large Class Activity: September 22}
\fancyhead[R]{\Large Fall 2014}
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\begin{document}
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\vspace*{0.2cm}

\ee{1} Mark the following True or False:
\begin{enumerate}[(a)]
\item \line(1,0){35}\;\;One need only record a few trials to be able to create a chart of probabilities and make accurate predictions. 
\item \line(1,0){35}\;\; Random phenomenon are outcomes that one cannot use probability arguments to predict possible outcomes. 
\item \line(1,0){35}\;\; Independent trials are events where one outcome does not influence any of the others.
\item \line(1,0){35}\;\; All probabilities are between 0 and 1.
\item \line(1,0){35}\;\; Disjoint events are events which are independent. 
\end{enumerate}

\vspace{2cm}

\ee{2} Krystina likes to cheat at dice games so she always brings a weighted dice. Her foul dice has the following probabilities: \\
\begin{center}
\begin{tabular}{|c||c|c|c|c|c|c|}
\hline Value & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
Probability & 0.1 & .25 & .20 & ? & .15 & 0.25 \\ \hline
\end{tabular}
\end{center}
\vspace{0.5cm}

\begin{enumerate}[(a)]
\item What is the probability of rolling a 4? \vfill

\item What is the probability of rolling a 1 or a 4? What is the probability of rolling a 2 or a 6? What is the probability of \emph{not} rolling a 3? \vfill

\item What is the probability of rolling a 7? The probability of the sum of two rolls being 7? \vfill
\end{enumerate}

\newpage

\ee{3} Given that $A$ and $B$ are independent events with $P(A)=0.7$ and $P(B)=0.4$, find:
\begin{enumerate}[(a)]
\item $P(A \text{ and }B)$

\vspace{2cm}

\item $P(B|A)$

\vspace{2cm}

\item $P(A \text{ or }B)$

\vspace{3cm}
\end{enumerate}

\ee{4} Real estate ads suggest that 64\% of homes for sale have garages, 21\% have swimming pools, and 17\% have both features.
\begin{enumerate}[(a)]
\item Find the probability that a home for sale has a swimming pool or a garage.
\vspace{4cm}

\item Find the probability that it has neither a swimming pool nor a garage. 
\end{enumerate}

\newpage
\ee{5} There are three airlines to get from Mayberry to Pawnee: Artin Lines, Stewart Air, or Albowitz Flights. If you take Artin, there is a 60\% chance your flight will be late, 50\% if you take Stewart, and a 20\% chance that you will be late if you take Albowitz. However, Artin services 50\% of the flights from Mayberry to Pawnee, Stewart handles 40\% of the flights, while Albowitz handles only 10\% of the flights. \\

\begin{enumerate}[(a)]
\item Draw a diagram illustrating the possible outcomes. \vfill
 
\item If you were to take a flight from Mayberry to Pawnee and were late, what is the probability that you took Artin? The probability that you took Albowitz? \vfill

\item If you took a flight from Pawnee to Mayberry and the flight was on time, what was the probability that it was Stewart? The probability that it was Albowitz? \vfill
\end{enumerate}

\end{document}