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Expected Value
Expected value is the probability-weighted average of every possible numerical outcome.
How it works
Expected value is the probability-weighted average of every possible numerical outcome. Name the quantities before calculating, keep each transformation logically equivalent, and check the result against the original conditions.
Worked example
A fair game pays 2 or 8 points. Find its expected value.
- Each payoff has probability 1/2.
- Compute (1/2)2+(1/2)8.
- Add the weighted values.
The expected value is 5 points.
Try it now
These questions come from the same validated skill generator used by the game.
Common mistakes
- Using a remembered formula without identifying what each symbol represents.
- Changing a value or condition during an intermediate step.
- Skipping the final substitution, estimate, or logical check.
Challenge
Create a three-outcome game with expected value zero.
Questions learners ask
What is the key idea in expected value?
Expected value is the probability-weighted average of every possible numerical outcome.
How should I check an answer?
Substitute it into the original conditions, check units and signs, and decide whether its size is reasonable.