Tree Diagrams
Map sequential outcomes with branches.
Key idea
Map sequential outcomes with branches.
In depth
A tree diagram lays out sequential events: each branch carries a probability, and the probability of a path is the product along it. Add the paths that give the event of interest.
Worked example
Draw two cards without replacement: P(two aces) = 4/52 × 3/51 ≈ 0.0045.
Real-world uses
- Working out the chances of two medical tests both being positive or of a two-stage game
Common mistake
Forgetting to update probabilities on the second stage when there is no replacement.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Tree Diagrams?
Map sequential outcomes with branches. It is a topic at the intermediate level in Probability & Statistics.
Where is Tree Diagrams used in real life?
Real-world examples: Working out the chances of two medical tests both being positive or of a two-stage game.
What should I learn before Tree Diagrams?
Make sure you are comfortable with Experimental vs Theoretical, the previous topic in Probability & Statistics.
What is a common mistake with Tree Diagrams?
Forgetting to update probabilities on the second stage when there is no replacement.
How can I practise Tree Diagrams?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Tree Diagrams?
Move on to Counting Principle next.
Related intermediate topics in Probability & Statistics
- Collecting Data and Sampling – Surveys, experiments and random sampling.
- Bias in Sampling – Systematic errors that make samples unrepresentative.
- Histograms – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
- Mean – The arithmetic average.
- Median – The middle value of an ordered list.