Mathematics · Probability
A proportion p of a large population has a particular disease. A random sample of k people is drawn from the population and their blood samples are combined. An accurate test applied to the combined sample shows a positive result, indicating at least one person has the disease. What is the probability that exactly one of the k people has the disease?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 11k
- 2pp + p2 + ... + pk
- 3(1 - p)k + kp(1 - p)k - 11 - (1 - p)k
- 4kp(1 - p)k - 11 - (1 - p)k✓
Correct answer
kp(1 - p)k - 11 - (1 - p)k
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