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Printjmc
counting and probability junior
Problem
Suppose you have a weighted coin in which heads comes up with probability and tails with probability . If you flip heads, you win 2 dollars, but if you flip tails, you lose 1 dollar. What is the expected value of a coin flip? Express your answer as a decimal.
Solution
By definition, we multiply the outcomes by their respective probabilities, and add them up: E = \frac34(+\2) + \frac14(-\1) = \1.50 - \0.25 = \boxed{\1.25}$.
Final answer
\$1.25