Conduct chance experiments; observed vs expected
Theory
The expected result of an experiment is the probability multiplied by the number of trials. The observed result is what actually happens — usually close to the expected result, but not identical.
The expected count is a prediction: \(\text{expected}=P\times\text{number of trials}\).
The observed count is what you actually tally. It varies from trial to trial, but the counts for all outcomes always add to the number of trials.
The more trials you carry out, the closer the observed counts usually sit to the expected ones.
Multiply the probability by the number of trials.
| Experiment | \(P\) | Trials | Expected |
|---|---|---|---|
| Coin, heads | \(\dfrac{1}{2}\) | \(40\) | \(20\) |
| Spinner, red | \(\dfrac{1}{4}\) | \(40\) | \(10\) |
| Spinner, blue | \(\dfrac{3}{4}\) | \(80\) | \(60\) |
How to find and use the expected result
- Write the probability of the outcome.
- Multiply it by the number of trials to get the expected count.
- Compare with the observed tally — expect small differences, not an exact match.
| \(\text{Expected}\) | \(=\) | \(\dfrac{1}{2}\times 40\) |
| \(=\) | \(20\) |
| \(\text{Expected}\) | \(=\) | \(\dfrac{1}{4}\times 40\) |
| \(=\) | \(10\) |
The counts add to \(100\).
| \(100-46\) | \(=\) | \(54\) |
| \(\text{Expected}\) | \(=\) | \(\dfrac{3}{4}\times 80\) |
| \(=\) | \(60\) |
Common pitfalls
Frequently asked questions
How do I work out the expected result?
Multiply the probability by the number of trials. For \(40\) coin flips, expected heads \(=\dfrac{1}{2}\times 40=20\).
Why don’t the observed results match the expected ones?
Chance varies from trial to trial, so the observed count is usually close to the expected count but not exactly equal.
Does more trials make it closer?
Usually yes. The more trials you carry out, the closer the observed counts tend to sit to the expected ones.
Do the observed counts still add up?
Yes. The observed tallies for all outcomes always add to the number of trials, even when each one differs from the expected count.