Smart Math guide · Statistics & Probability

Think in Expected Value

Expected value is a probability-weighted average of possible outcomes, useful for repeated decisions.

All levelsWorked example includedSelf-check included
The method

How to use it

  1. List outcomes.
  2. Multiply each outcome by its probability.
  3. Add the products.
Worked example

See it in action

50% chance of $10 and 50% chance of $0 gives EV=$5.

Check your thinking

How to verify it

Across many repeats, average payout should trend toward $5.

Watch out

Common mistake

Expected value is a long-run average, not a guarantee for one trial.