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\begin{document}
\title{Math 101 Homework}
\author{Mary Radcliffe}
\date{due 27 Jan 2017}
\maketitle

Complete the following problems. Fully justify each response.

\begin{enumerate}

\item Let $X$ be the probability space of 4 flips of a weighted coin, that has $\p{H} = 3/4$ and $\p{T}=1/4$. Let $A$ be the event that the outcome has at least 2 heads. Determine $\p{A}$.

\item Let $X$ be the probability space of 3 flips of a weighted coin, that has $\p{H} = p$ and $\p{T}=1-p$. Show carefully that the three events $A_1 = \{\hbox{first flip is H}\}$, $A_2 = \{\hbox{second flip is H}\}$, and $A_3 = \{\hbox{third flip is H}\}$ are mutually independent.

\end{enumerate}

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