Probability — domain overview
Probability accounts for roughly 10% of marks in AQA GCSE Maths 8300 and spans 9 specific points (P1–P9). It is an area where systematic method earns full marks even if your final answer differs from the expected value.
The probability spec at a glance
| Code | Topic | Core skill |
|---|---|---|
| P1 | Record, describe, analyse outcomes | Sample space diagrams, frequency, relative frequency |
| P2 | Probability scale and outcomes | 0 to 1 scale, all outcomes sum to 1 |
| P3 | Mutually exclusive and exhaustive | P(A) + P(not A) = 1; listing all outcomes |
| P4 | Independent and dependent events | Tree diagrams with replacement; without replacement |
| P5 | Tree diagrams | Multiply along branches; add across outcomes |
| P6 | Venn diagrams and sets | Union, intersection, complement |
| P7 | Conditional probability | P(A |
| P8 | Experimental vs theoretical | Relative frequency; increasing trials → closer to theoretical |
| P9 | Expected frequency | Expected = P × n |
The core rules
Addition rule (mutually exclusive events)
$$P(A ext{ or } B) = PA + PB$$ This only works when events cannot both happen.
Multiplication rule (independent events)
$$P(A ext{ and } B) = PA imes PB$$ This only works when events do not affect each other (with replacement or separate events).
Complement
$$P( ext{not } A) = 1 - PA$$
Conditional probability
$$P(A | B) = dfrac{P(A ext{ and } B)}{PB}$$
Tree diagrams
- Multiply along branches (AND)
- Add across outcomes (OR)
- Check: all branches from a node must sum to 1
- With replacement → same probabilities on second branch
- Without replacement → denominator decreases
Venn diagram notation
| Symbol | Meaning |
|---|---|
| A union B | A or B (union) |
| A intersection B | A and B (intersection) |
| A' (complement) | Not A |
| xi (universal set) | Everything |
Common exam mistakes
- Adding when you should multiply — "both events occur" means AND → multiply
- Not updating the denominator — in without-replacement problems, total reduces by 1 for the second draw
- Treating dependent events as independent — drawing without replacement changes probabilities
- Missing outcomes in a tree — always check branch pairs sum to 1
- Relative frequency ≠ probability — it is an estimate; more trials → more accurate estimate
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