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Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them. What is the expected value of the number shown when we draw a single slip of paper?

 Aug 5, 2021
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Expected value is computed by multiplying all of the possible outcomes by their probabilities, and then summing. $8/10$ of the time we draw a 3 and $2/10$ of the time we draw a 9. Therefore the expected value is \[3\cdot\frac{8}{10} + 9\cdot\frac{2}{10} = \boxed{\frac{21}{5}}.\]

 Aug 5, 2021

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