What you'll learn
How to find probabilities involving two or more events.
Key rules
- Mutually exclusive events cannot happen together: P(A or B) = P(A) + P(B).
- Independent events do not affect each other: P(A and B) = P(A) × P(B).
- General AND = multiply along tree branches; OR = add the relevant outcomes.
Tree diagrams
- Branches from each node sum to 1.
- Multiply along branches for combined outcomes; add outcomes for 'or'.
- For without replacement, the second set of probabilities changes (conditional).
Exam tips
- Read carefully whether events are with or without replacement.
- Label tree diagrams fully with probabilities.
Common mistakes
- Adding when you should multiply (and vice versa).
- Forgetting probabilities change in 'without replacement' problems.