Tree diagrams: GCSE Maths revision
A tree diagram shows sequential events. Multiply along a branch, add different routes that count as the same outcome.
With and without replacement
Independent (with replacement, or separate trials): probabilities on the second set of branches stay the same. Dependent (without replacement): they change.
Try these questions
Cover the answers and have a go first. Worked solutions are underneath.
A coin twice. P(two heads)?
P(A) = 0.4 independent of P(B) = 0.5. P(both)?
Bag: 3 red, 2 blue. Two sweets without replacement. P(both red)?
Common mistakes
- Adding along a branch instead of multiplying.
- Using the same second-branch probabilities when the first item was not replaced.
Answers and working
Frequently asked questions
When do I add probabilities?
When you have alternative routes (OR). Multiply for AND along one route.
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