Knowledge Organiser: Combined Events
This topic summary covers Knowledge Organiser: Combined Events within Combined Events for GCSE Mathematics. Revise Combined Events in Probability for GCSE Mathematics with 11 exam-style questions and 2 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 5
Practice
11 questions
Recall
2 flashcards
Knowledge Organiser: Combined Events
Key Terms
- Independent events: One event does not affect the probability of the other
- Dependent events: One event changes the probability of the other
- Mutually exclusive: Events that cannot both happen at the same time
- P(A and B): Probability that both A and B occur
- P(A or B): Probability that at least one of A or B occurs
- P(B|A): Conditional probability — probability of B given A has occurred
Must-Know Facts
- "And" means multiply probabilities
- "Or" (for mutually exclusive events) means add probabilities
- For mutually exclusive events: P(A or B) = P(A) + P(B)
- If events can overlap, subtract the intersection to avoid double-counting
- For independent events: P(A and B) = P(A) × P(B)
- For dependent events: P(A and B) = P(A) × P(B|A)
- Use a tree diagram to organise multi-stage problems
Key Formulas
- P(A and B) = P(A) × P(B) — for independent events
- P(A and B) = P(A) × P(B|A) — for dependent events
- P(A or B) = P(A) + P(B) − P(A and B) — addition rule
- P(A or B) = P(A) + P(B) — only when mutually exclusive
Common Mistakes
- Adding for "and": P(A and B) = P(A) × P(B) for independent events — multiply, don't add
- Forgetting to subtract overlap for "or": P(A or B) = P(A) + P(B) − P(A and B) unless mutually exclusive
- Assuming independence: Check whether events are independent (e.g. with replacement) or dependent (without replacement)
- Mutually exclusive vs independent: Mutually exclusive means they cannot both happen; independent means one does not affect the other — these are different concepts
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Practice Questions for Combined Events
A fair coin is flipped and a fair die is rolled. What rule is used to find P(heads AND rolling a 3)?
Explain the difference between independent and dependent events in probability. Give an example of each.
Quick Recall Flashcards
11 questions on Combined Events — practise free
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