StatisticsdrillBayes: a positive screening result
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
Suppose a screening test checks patients for a condition. 0.5% of items are affected. The screen flags 85% of affected items (sensitivity) and correctly clears 99% of the others (specificity). A patient is flagged. What is the probability it is really affected? Round to 4 decimal places.
What this problem teaches
The formula: P(D | +) = P(+ | D) P(D) / [ P(+ | D) P(D) + P(+ | not D) P(not D) ]. When the condition is rare, most flags are false alarms even with an accurate screen.
A hint if you get stuck
P(true | flagged) = true flags / all flags. All flags = prevalence × sensitivity + (1 - prevalence) × (1 - specificity).
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