Consider a disease that is on average caught by 1 in N people. Let's say that a disease

Shea Stuart 2022-07-01 Answered
Consider a disease that is on average caught by 1 in N people. Let's say that a disease test gives a false positive for p % of healthy people. For diseased people, it always gives a correct, positive answer.
What's the chance that a person who got a positive result is healthy?
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Answers (1)

Leslie Rollins
Answered 2022-07-02 Author has 25 answers
Imagine 1000 N people. 1000 N N = 1000 of those people have the disease, 1000 N 1000 = 1000 ( N 1 ) do not. Of the 1000 ( N 1 ) people who do not have the disease the test falsely reports that 1000 p ( N 1 ) do have the disease. The test also reports all 1000 people who have the disease so reports a total of 1000 + 1000 p ( N 1 ) = 1000 ( 1 + p ( N 1 ) ) people as having the disease. Of the 1000 ( 1 + p ( N 1 ) ) people reported to have the disease, 1000 p ( N 1 ) are actually healthy. The probability that a person reported to have the disease is actually healthy is 1000 p ( N 1 ) 1000 ( 1 + p ( N 1 ) ) = p ( N 1 ) ( 1 + p ( N 1 ) ) .

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