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{\bf Worksheet \#21; date: 11/07/2018}
{\bf MATH 55 Discrete Mathematics}
\begin{enumerate}
\item {\em (Rosen 7.1.6)} What is the probability that a card selected at random from a standard deck of $52$ cards is an ace or a heart?
\item {\em (Rosen 7.1.30)} What is the probability that a player of a lottery wins the prize offered for correctly choosing give (but not six) numbers out of six integers chosen at random from the integers between $1$ and $40$, inclusive?
\item What is the probability that a player wins prize above and do not need to split it with anyone else, if there are a million players in total?
\item Suppose we randomly generate a number by summing two independence die rolls. How many possible numbers can we generate? Explain why the probability of getting an $8$ is not simply $1 / N$ where $N$ is the number of possible outcomes.
\item {\em (Rosen 7.2.16)} Show that if $E$ and $F$ are independent events, then $\bar{E}$ and $\bar{F}$ are also independent events.
\item A fair coin is tossed $5$ times. What is the probability of the first two being heads if it is known there are only two heads in total?
\item {\em (Challenging and confusing)} Suppose we ring the door bell of a family with two children. A young girl answers the door. What is the probability of the other child also being a girl?
\end{enumerate}
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