M5.4 Outcomes and Probability
Probability vocabulary and scale, systematic outcome listing, equally likely events, complements, mutually exclusive outcomes and expectation.
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
Probability runs from 0 to 1 and the probabilities of all mutually exclusive exhaustive outcomes sum to 1.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Systematic lists, tables or diagrams prevent omissions when events are combined.
Exam cue: Define the complete outcome set before calculating, then express the answer as a fraction or decimal in the permitted form.
Concept 3
Expected frequency is a long-run prediction found by multiplying probability by the number of trials.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Adding probabilities for events that can occur together or assuming outcomes are equally likely without justification.
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
Outcome
A possible result of an experiment or event.
Sample space
The complete set of possible outcomes.
Mutually exclusive
Events that cannot occur together in one trial.
Complement
The event that the stated event does not occur.
Equally likely
Having the same probability of occurring.
Expected frequency
The predicted count, equal to probability multiplied by number of trials.
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 fair die is rolled. What is P(number greater than 4)?
A bag has 5 red, 3 blue and 2 green counters. Find P(not blue).
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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