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4.  After putting your favorite CD in your CD player, you set the player to\\
\ \ \ \ shuffle mode, which plays all the songs on the disc in random order, but\\
\ \ \ \ still never repeats a song. There are 13 songs on the disc, of which you\\
\ \ \ \ like 10.\\
\ \\
\ \ \ \ (a) What is the probability that you like the first song?\\
\ \ \ \ (b) What is the probability that you like the first two songs?\\
\ \ \ \ (c) What is the probability that you don't like the second song?\\
\ \\
\ \\
5. Suppose Matt finds 7 cans, all with their labels torn off. He can\\
\ \ \ \ remember that 2 contain pineapple, while the rest contain tomatoes.\\
\ \ \ \ Hoping to make some spagetti sauce, he decides to open 3 cans at\\
\ \ \ \ random.\\
\ \\
\ \ \ \ (a) How many ways are there for him to choose the 3 cans?\\
\ \ \ \ (b) How many ways are there for him to choose the 3 cans, with\\
\ \ \ \ \ \ \ \ \ \ exactly 2 containing tomatoes?\\
\ \ \ \ (c) What is the {\em probability} of at least 2 containing tomatoes?\\
\ \\
\ \\
6. Inside a bag is a bunch of balls with numbers on them.  Four have 0 on\\
\ \ \ \ them, three have 1, two have 2, and one has 3.  Two balls are drawn at\\
\ \ \ \ random, one at a time. Let X be the random variable which is the\\
\ \ \ \ number on the first ball {\em minus} the number on the second ball.\\
\ \\
\ \ \ \ (a) What are the possible outcomes for X?\\
\ \ \ \ (b) What the the probability distribution function $f(x)$?\\
\ \\
\ \\
7. For a given STAT class, the probability of getting a certan number of\\
\ \ \ \ points out of 30 on the exam is given by the follow distribution function:\\
\ \\
\ \ \ \ (a) Find the $\mbox{Expected value of X}=E[X]=\mu$.\\
\ \ \ \ (b) Find the $\mbox{Variance of X}=V[X]=\sigma^{2}$.\\
\ \ \ \ (c) Find the $\mbox{Standard Deviation of X}=\sigma$.\\

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