Theoretical vs experimental probability
Edexcel distinguishes two routes to a probability:
- Theoretical — based on equally-likely outcomes (e.g. fair dice).
- Experimental (relative frequency) — based on observed data, used when outcomes are not equally likely or unknown.
The probability scale
All probabilities are between 0 and 1 (or 0% to 100%):
- 0 = impossible.
- 0 < p < 0.5 = unlikely.
- 0.5 = even chance.
- 0.5 < p < 1 = likely.
- 1 = certain.
Probabilities can be written as fractions (1/6), decimals (0.167), or percentages (16.7%).
Theoretical probability
For an equally-likely sample space:
P(event) = (number of favourable outcomes) ÷ (total number of outcomes).
Example: P(odd number on a fair dice) = 3/6 = 1/2.
Relative frequency (experimental probability)
P(event) ≈ frequency of event ÷ total trials.
Example: A drawing pin is dropped 200 times. It lands point-up 132 times. Estimated P(point up) = 132/200 = 0.66.
This estimate improves with more trials (P5).
When to use which
| Situation | Use |
|---|---|
| Coin, dice, deck of cards (assumed fair) | Theoretical |
| Drawing pin, biased coin, broken machine | Relative frequency |
| Real-world events from past data (rain, accidents) | Relative frequency |
Edexcel exam tip
If a question gives no symmetry argument (no fair dice, no equal sectors), Edexcel expects relative frequency. The phrase "estimate the probability" is the giveaway — theoretical is the exact value, never an estimate.
⚠Common mistakes— Common errors
- Computing relative frequency from a small sample and treating it as exact.
- Writing P > 1 or P < 0 — impossible.
- Confusing percentages with decimals: 0.05 ≠ 5/100 in some calculations.
- Forgetting the sum of all probabilities = 1.
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