Conditional Probability and Counting
Reason with conditional samples, independence, product rules and systematic counting.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Conditional probability
Exam cue: Restrict the denominator to the stated condition, decide whether earlier outcomes change later probabilities and count independent choices systematically.
Concept 2
Independent and dependent events
Exam cue: State the conditioned sample space and compare an alternate table, tree or enumeration.
Concept 3
Product rule for counting
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation core with Higher-tier extensions
Formal conditional probability, algebraic dependence and the product rule for counting are Higher-only extensions of shared combined-event reasoning.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Using the original total as the denominator after a condition has restricted the sample.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Conditional denominator
Count only outcomes satisfying the stated condition.
Independent events
One event does not change the probability of the other.
Product rule for counting
Multiply the numbers of independent choices at successive stages.
Conditional Probability and Counting: method
Restrict the denominator to the stated condition, decide whether earlier outcomes change later probabilities and count independent choices systematically.
Conditional Probability and Counting: check
State the conditioned sample space and compare an alternate table, tree or enumeration.
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
Higher · AO1 technique · Non-calculator — Of 30 students who play a school sport, 18 play football. Find P(football | plays a sport).
Higher · AO2 reasoning · Either paper — A card is known to be red in a standard 52-card deck. Find P(it is a heart).
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”