Tree diagrams and combined events · Year 12
In Year 12 you get fluent with: without replacement.
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.
- Without replacement (dependent events), the numbers change after the first pick.
- P(at least one) = 1 − P(none).
Worked examples
Example 1
A driver passes two sets of traffic lights. Each is red with probability 0.4, independently. Find P(both red) and P(exactly one red).
Answer: 0.16 and 0.48
Example 2
A drawer has 5 black and 3 white socks. Two are taken without looking. Find the probability they are the same colour.
Answer: 13/28