Theoretical vs experimental probability
WJEC contrasts two ways of measuring probability:
Theoretical probability
Calculated from the model: equally likely outcomes ⇒ P(event) = favourable ÷ total.
- P(rolling a 6 on a fair dice) = 1/6.
- P(red card in standard 52-card deck) = 26/52 = 1/2.
Experimental (relative) probability
Estimated from data: P(event) ≈ (observed frequency) ÷ (number of trials).
If a coin lands heads 47 times in 100 tosses, experimental P(heads) = 47/100 = 0.47.
Why they differ
Random variation. With small samples, experimental probability often differs noticeably from theoretical. As trials → ∞, experimental → theoretical (the Law of Large Numbers).
Estimating expected frequency
Once experimental P is established, multiply by new trials:
If a biased coin gives P(heads) = 0.47 from 100 trials, expected heads in 500 future tosses ≈ 0.47 × 500 = 235.
Detecting bias
Compare experimental P to the theoretical P from a fair model:
- Big gap + many trials → likely biased.
- Small gap + few trials → could be coincidence.
0–1 probability scale
All probabilities lie 0 ≤ P ≤ 1.
- 0 → impossible.
- 1 → certain.
- 0.5 → equally likely.
- Probabilities are written as fractions, decimals, or percentages — but never ratios (so write 1/4 or 0.25 or 25%, not "1 in 4" in formal answers).
WJEC exam tip
When calculating expected frequency from data, use the experimental probability (the observed proportion), not the theoretical 1/6 or 1/2 — that's the whole point of the question.
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