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COMPUTER SCIENCE 20, SPRING 2012 \\
DISCRETE MATHEMATICS FOR COMPUTER SCIENCE\\
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Class \#26 (Bayes Theorem)
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\paragraph{Homework, due in hard copy Monday 4/16/2012 at 10:10am}
\paragraph{Please write your TF's name on your homework, and list the names of any students with whom you collaborated.}
\begin{enumerate}
\item Our CS 20 class has 42 students. Assume that the birthday of the students are independent uniform random variables and that nobody was born on Feb 29.
\begin{enumerate}
\item What is the probability that a given pair of students in the class shares the same birthday? Give your answer as a decimal to 3 decimal places.
\item What is the probability that there exists a pair of students in the class that has the same birthday? Give your answer as a decimal to 3 decimal places.
\item A student is a ``lonely student'' if no other student shares his/her birthday. What is the expected number of lonely students in the class? Give your answer as a decimal to one decimal place.
\end{enumerate}
\end{enumerate}
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