Expected Value and Risk
Ages 16–18Difficulty adapts to you
Expected Value and Risk
Expected value is the long-run mean result: multiply each outcome by its probability and add. It does not predict the result of one trial. A fair game can have expected value zero while individual players still win or lose.
Your goals
- ✓You can use expected value to compare repeated random outcomes and understand risk.
- ✓You can use Expected Value and Risk, model correctly.
- ✓You can use the definitions, units, assumptions, and examples to check your answer.
Words to know
- Expected Value and Risk:
- Use expected value to compare repeated random outcomes and understand risk.
- model:
- A rule or representation used to describe a situation and make a prediction.
Examples
- 1A game pays ₦100 with probability 0.2 and ₦0 otherwise; expected winnings are 0.2 × 100 = ₦20.
- 2Subtract the entry fee from expected winnings to find expected profit.
Check these
- • Do not skip the meaning of a term or give a result without explaining what it means.
- • Keep every number, symbol, label, and unit in its correct place.
- • Show enough working to check how you reached your answer.
Helpful habits
- • Read the whole question before choosing what to do.
- • Show one clear step at a time and check each step.
- • If you are stuck, draw a model, try smaller numbers, or revisit the example.
Now try your own
Create your own expected value and risk example, solve it, and explain how you checked it.
Professor Wise Owl
Wisdom & Understanding“Mistakes are proof that you are trying. Keep going!”