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.
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
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
What are independent events?
Events where one event doesn't affect the probability of the other
For independent events, what is P(A and B)?
P(A and B) = P(A) × P(B)