A tree diagram shows two events one after the other. Each branch is labelled with its probability, and the branches from one point add up to 1.
To find the probability of a path, multiply along the branches. To combine several paths, add their probabilities. For a fair coin flipped twice, P(two heads) = 1/2 × 1/2 = 1/4, and P(at least one head) = 1 − P(no heads) = 1 − 1/4 = 3/4.
Worked example
A fair coin is flipped twice. What is the probability of one head and one tail?
- Two paths: HT and TH. Each is 1/2 × 1/2 = 1/4.
- Add the paths: 1/4 + 1/4.
Answer:1/2
Key words
- branch
- a line for one outcome
- multiply along
- for 'and' on one path
- add down
- for 'or' across different paths
Practise this
New questions every time.
Common Core-referenced: 7.SP.C.8b