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Prof.~David Draper \\
Department of \\ 
\hspace*{0.1in} Applied Mathematics and Statistics \\
University of California, Santa Cruz

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\textbf{\large AMS 131: Quiz 1}

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Name: \underline{\hspace*{5.0in}}

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(You can use the back of this page if necessary in any or all parts of the
problem.)

In (a) and (b) below, say whether the statement is true, false, or
meaningless, and explain briefly in each case.

\begin{itemize}

\item[(a)] 

If something has probability $-1$, it can't happen.

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\item[(b)] 

If something has probability 0.8, it can be expected to happen about four
times as often as its opposite.

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\end{itemize}

\begin{itemize}

\item[(c)] 

Two cards will be dealt off the top of a well-shuffled standard deck of 52 playing cards (without replacing the first card). You have a choice:

\begin{itemize}

\item[(i)]

To win \$1 if the first card is an ace (there are four aces in a standard deck).

\item[(ii)]

To win \$1 if the first card is an ace, and the second card is an ace.

\end{itemize}

Briefly explain which is better, intuitively and without calculating, and then work out both probabilities.

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\item[(d)] 

Two cards will be dealt off the top of a well-shuffled deck (without
replacing the first card). You have a choice:

\begin{itemize}

\item[(i)]

To win \$1 if the first card is a club (there are 13 clubs in a standard deck).

\item[(ii)]

To win \$1 if the first card is a club, or the second card is a diamond (there are 13 diamonds in a standard deck, and a card cannot be both a club and a diamond).

\end{itemize}

Briefly explain which is better, intuitively and without calculating, and then work out both probabilities.

\end{itemize}

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