Track 4 · Probability · Lesson 5 of 9
Multiplication rule and probability trees
Use the general multiplication rule and probability trees to find probabilities of sequences of events, and combine branches with the law of total probability.
A retailer buys the same part from two suppliers with different defect rates. What fraction of parts on the shelf are defective? Questions like this — where what happens next depends on what happened first — are solved by drawing a probability tree and multiplying along its branches.
Many situations unfold in stages: a part comes from a supplier, then it is defective or not; a customer adds an item to the basket, then checks out or not. The probability of the second stage usually depends on the first. The tool for this is the general multiplication rule.
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It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Apply the general multiplication rule P(A ∩ B) = P(A)P(B | A)
- Build a probability tree with conditional branch probabilities that sum to 1
- Use the law of total probability as a weighted average of conditional probabilities
- Handle sampling without replacement by updating the second-stage probabilities