4.3 Probability - single event/experiment
Represent theoretical and experimental probability for one event and use repeated trials to evaluate a model.
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 probability language, the 0-to-1 scale and equivalent numerical forms.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Calculate theoretical probabilities from equally likely outcomes.
Exam cue: Define the outcome set and denominator before calculating or estimating the probability.
Concept 3
Estimate probability from relative frequency and compare experimental with theoretical results.
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
Using words such as likely or unlikely when a numerical probability is required, or treating experimental frequency as exact theory.
Guardrail: The Unit 1 and Unit 3 lists are limited and Unit 2 supplies none; preserve exact values and know all other required relationships.
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
Probability scale
Probability ranges from zero for impossible to one for certain.
Theoretical probability
Theoretical probability follows from a model of outcomes.
Relative frequency
Relative frequency is event frequency divided by number of trials.
Complement
The complement probability is one minus the event probability.
Fair experiment
A fair experiment gives intended outcomes equal chances where the model requires it.
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
An event has probability 0.37. What is the probability that it does not occur?
Which listed number is outside the permitted range for a probability?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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