M7.4 Counting and Independent Probability
Product rule for counting, addition for mutually exclusive events, multiplication for independent events and independent tree diagrams.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
The product rule counts ordered multi-stage choices by multiplying the number of choices at each stage.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Mutually exclusive alternatives add because they cannot occur together.
Exam cue: Label every branch, decide whether the connector means and or or, then combine path probabilities accordingly.
Concept 3
Independent successive events multiply because one result does not change the next event's probability.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Using the original probability on a without-replacement tree where events are not independent.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Product rule for counting
Multiply the choices at successive stages to count combined outcomes.
Independent events
Events for which one outcome does not change the probability of another.
Addition rule
Add probabilities for mutually exclusive alternatives.
Multiplication rule
Multiply probabilities along an independent sequence.
Tree diagram
A branching display of successive outcomes and their probabilities.
Path probability
The product of branch probabilities along one route through a tree.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
4 shirts and 3 trousers give outfits?
P(A)=0.3,P(B)=0.5 independent. P(both)?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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