Edexcel International GCSE Mathematics A · 4MA1
Probability trees
A probability tree organises sequences of events. Multiply along a complete path to find the probability of that sequence, then add mutually exclusive paths for the required event. Sampling without replacement changes the probabilities at the next stage.
Key method
Branches from each point sum to 1. After an item is removed, update both the relevant count and total count before drawing the next branches.
Worked example
A bag has 3 red and 2 blue counters. Two are taken without replacement. Find P(both red).
- The first-red probability is 3/5.
- After removing a red, 2 red counters remain out of 4 counters, so P(second red | first red) = 2/4.
- Multiply along the red–red path.
Answer and interpretation
(3/5)(2/4) = 3/10.
Common mistake
Using 3/5 for the second draw treats the sample as if the counter had been replaced.
Practise independently
Find the probability of one counter of each colour in either order.
Check your answer
(3/5)(2/4) + (2/5)(3/4) = 3/5.
Syllabus connection
This lesson develops tree diagrams within the probability area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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