Tree diagrams and combined events · Year 9
In Year 9 you learn: tree diagrams.
A tree diagram shows every outcome of two or more events, one stage after another. Multiply along the branches to get the probability of a path. Then add the paths that give the outcome you want.
Key facts
- Branches from the same point add up to 1.
- Multiply along the branches for “this and then that”.
- Add the probabilities of different paths for “this path or that path”.
- Independent events: the second-stage probabilities are the same on every branch.
- P(at least one) = 1 − P(none).
Worked examples
Example 1
P(rain) = 0.3. If it rains, P(late) = 0.5. If it is dry, P(late) = 0.1. Find P(late), and P(rain | late) to 3 decimal places.
Answer: 0.22; 0.682