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counting and probability intermediate
Problem
A very bizarre weighted coin comes up heads with probability , tails with probability , and rests on its edge with probability . If it comes up heads, I win 1 dollar. If it comes up tails, I win 3 dollars. But if it lands on its edge, I lose 5 dollars. What is the expected winnings from flipping this coin? Express your answer as a dollar value, rounded to the nearest cent.
Solution
The expected value is E = \left(\dfrac{1}{2}\times\1\right) + \left(\dfrac{1}{3}\times\3\right) + \left(\dfrac{1}{6}\times(-\5)\right) = \\dfrac{4}{6} =\boxed{\\dfrac23 \approx \0.67}.
Final answer
\\dfrac23 \approx \0.67