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Break-even with a fee

Expected valueEasy

A trade makes $45$ if it works and loses $15$ if it fails, and a fee of $5$ is due either way. Passing makes $0$ . At what posterior chance of working are you exactly indifferent? Give a fraction.

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Hint

Set the expected value of trading to zero.

Solution

With chance $p$ of working, the expected value is $45 p - 15 (1 - p) - 5$ , which equals $60 p - 20$ .
Setting it to zero gives $p = \frac{20}{60} = \frac{1}{3}$ .

Answer: $\frac{1}{3}$

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