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counting and probability intermediate
Problem
A certain coin is weighted such that the chance of flipping heads is and the chance of flipping tails is . Suppose that we win \3\ if we flip tails. What is the expected value, in dollars, of our winnings after one flip? Express your answer as a common fraction.
Solution
In one flip, we have a chance of getting heads and winning 3 dollars, and a chance of getting tails and losing 2 dollars. So the expected value of one flip is E = \frac{1}{3}(\3) + \frac{2}{3}(-\.
Final answer
-\frac{1}{3}