Beyond Common Core
Problem 24 of 45s12-024
In a group, 5% have a condition. A test is positive for 90% of those with it and 10% of those without it. Someone tests positive. What is the probability they have it?
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Solution walkthrough2:11
- Draw a tree: first has it () or not (), then positive or negative given each branch.
- Multiply along each positive path: and .
- Total probability: , adding the two paths that end in a positive.
- Given a positive, take the true-positive share: .
- In people: true positives, false positives. Only of the positives have it.
- Traps: is , is not divided, and is itself.