Tree Diagrams and Combined Events
A tree diagram lists every outcome of combined events, with probabilities multiplied along branches and added across outcomes.
▶ Interact
Play with the controls to see the idea in action.
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A tree diagram lists every outcome of combined events, with probabilities multiplied along branches and added across outcomes.
- Multiply along the branches
- Add the ends that match the question
- Without replacement changes later probabilities
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Tree Diagrams and Combined Events?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Tree Diagrams and Combined Events. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Tree Diagrams and Combined Events in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Tree Diagrams and Combined Events gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Tree Diagrams and Combined Events in detail
A tree diagram shows the outcomes of two or more events in stages, with branches labelled by probabilities. You multiply along the branches to find the probability of a path (and), and add the probabilities of different paths that give the same result (or).
For events without replacement, such as picking two sweets from a bag, the probabilities on the second set of branches change because the total number has decreased. Tree diagrams help avoid missing outcomes and are used for sequences of decisions, tests and quality control.
How the interactive helps you understand Tree Diagrams and Combined Events
Watch the probability model in the interactive. Use any sliders or buttons it offers to change the values and see how the probability model responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Tree Diagrams and Combined Events.
Real-life uses and examples
- Use Tree Diagrams and Combined Events when comparing prices, discounts or recipe quantities in everyday life.
- Explain Tree Diagrams and Combined Events to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Tree Diagrams and Combined Events in exam questions, where it often sits inside a short word problem.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Tree Diagrams and Combined Events.
- Memorising the steps for Tree Diagrams and Combined Events without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Tree Diagrams and Combined Events
What is Tree Diagrams and Combined Events?
A tree diagram lists every outcome of combined events, with probabilities multiplied along branches and added across outcomes.
What are the most important points about Tree Diagrams and Combined Events?
The main points are: Multiply along the branches; Add the ends that match the question; Without replacement changes later probabilities.
Why is Tree Diagrams and Combined Events useful?
Understanding Tree Diagrams and Combined Events gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Tree Diagrams and Combined Events?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Tree Diagrams and Combined Events?
Related topics in Mathematics include Mean, Median and Mode, Bar Charts and Pictograms, Scatter Graphs and Correlation.