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\begin{header}
\psheader{- Week 14}{12}{11:59PM}{Sunday}
\end{header}

\begin{itemize}
\item You may work in groups of size up to 3.  Note that you are
  all responsible for what you turn in and when you turn it in.
\end{itemize}

\begin{enumerate}
\item \problem{3}{Dice}
  \begin{enumerate}
  \item A pair of 6-sided dice are rolled.  What is the probability
    that both dice show an even number?  Do this problem by defining
    a sample space of equally likely outcomes and calculating the
    probability as a ratio of the cardinality of the event and the
    cardinality of the sample space
  \item A pair of 6-sided dice are rolled.  What is the probability
    that exactly one die shows an even number?  Do this problem by
    defining a sample space of equally likely outcomes and calculating
    the probability as a ratio of the cardinality of the event and the
    cardinality of the sample space.
  \item A pair of 6-sided dice are rolled.  What is the probability
    that the sum of the dice rolls is even?
  \end{enumerate}
\item \problem{9}{Cards}
  A standard deck of cards has 52 cards in 4 suits (diamonds, hearts, clubs, and spades).  Each suit has 13 ranks (2-10, J, Q, K, A).
  \begin{enumerate}
  \item If I shuffled a deck of cards, how likely am I to draw a 2 of any suit?
  \item If I shuffled a deck of cards and drew the 2 of Spades, how likely am I to pull a 2 of any suit on my next draw?
  \item What are the odds overall of drawing two 2s in a row from a freshly shuffled deck?
  \item If I shuffled a deck of cards and drew five cards in a row, what is the probability that every card has the same suit?
  \item If I shuffled a deck of cards and drew five cards in a row, what is the probability that every card has the same rank?
  \item You draw two cards.  What are the odds that their sum is exactly 18?  Consider J=Q=K=10, A=1.
  \item You draw two cards.  What are the odds that they include at least one face card (J/Q/K)?
  \item You draw two cards.  What are the odds that they include at least one face card (J/Q/K) and they sum up to 18?
  \item You draw two cards, and your psychic tells you they add up to 18.  What are the odds that at least one of your cards is a face card?  Write your answer as an expression using P(x), P(x and y), and/or P(x|y), then substitute in the relevant values from the preceding questions to compute the answer.
  \end{enumerate}

\end{enumerate}

\end{document}
