Option A pays 50 dollars for sure. Option B pays 100 dollars with probability 3/5 and nothing otherwise. By how many dollars does the expected value of B exceed that of A?

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Option A pays $50$ dollars for sure. Option B pays $100$ dollars with probability $\frac{3}{5}$ and nothing otherwise. By how many dollars does the expected value of B exceed that of A?

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Hint

Compute each expected value separately.

Solution

Option A has expected value $50$ .
Option B has expected value $\frac{3}{5} \times 100 = 60$ .
The difference is $60 - 50 = 10$ .

Answer: $10$

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