Question

A medical test for disease D has outcome positive or negative with following probabilities. Suppose you go for a test and get a positive. What is the probability that you have a disease?

Source: All of Statistics by Larry A. Wasserman

##          Disease No.Disease
## positive  0.0081      0.090
## negative  0.0090      0.901

Answer

From conditional probability:

\[P(Disease|positive) = \frac {P(positive \cap Disease)} {P(positive)}\] \[P(Disease|positive) = \frac {0.0081}{0.0081+0.090}\] \[P(Disease|positive) \approx 0.08\]

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