4.4 Probability - more than one event/experiment
Enumerate compound outcomes and combine mutually exclusive, independent and dependent probabilities correctly.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Use addition for mutually exclusive alternatives and multiplication for independent events.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
List combined outcomes systematically using tables, diagrams and trees.
Exam cue: Decide whether the events are alternatives or a sequence and whether probabilities change between stages before combining them.
Concept 3
Solve repeated-event and sampling-without-replacement problems at the specified tier.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 2. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Multiplying probabilities that are not independent or replacing a probability incorrectly after an outcome without replacement.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Mutually exclusive
Mutually exclusive events cannot occur together.
Independent
Independent events do not change one another's probabilities.
Dependent
For dependent events, later probabilities depend on earlier outcomes.
Tree diagram
A probability tree displays sequential branches and conditional probabilities.
Without replacement
Without replacement changes the population and later probabilities.
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
A five-counter bag contains three red and two blue. On two non-replacement draws, calculate the chance the colours differ.
Among 40 people, 18 are in A, 15 in B and 6 in both. How many are in A∪B?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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