Probability trees
Objective. Represent two-stage experiments with tree diagrams.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A probability tree diagram represents the outcomes of two or more linked events as branching paths, with each branch labelled with its own probability. To find the probability of a combined outcome following one path through the tree, multiply the probabilities along that path together. To find the probability of several different paths satisfying a condition, calculate each path's probability separately and add them together. For example, if the probability of rain is 0.3 and, given rain, the probability of being late is 0.6, the combined probability of both rain and being late is 0.3 × 0.6 = 0.18.
Worked example
A probability tree shows a spinner landing on red with probability 0.4, then a coin landing on heads with probability 0.5. Find the probability of red followed by heads.
- 1Identify this as a single path through the tree, requiring both events to happen.
- 2Since both events occur together, multiply their probabilities.
- 3Substitute the given values: 0.4 × 0.5.
- 40.4 × 0.5 = 0.2.
Answer: 0.2
Concept mastery
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Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes add probabilities along a single path instead of multiplying them, treating 'and' events as if they were 'or' events. Multiply probabilities along a single branch path; only add when combining separate paths.
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