im sure i followed it correctly but my answer is unusually small...(adsbygoogle = window.adsbygoogle || []).push({});

1 in a thousand people have a disease. A company has discovered a new method for testing for the disease.

If a person has the disease, the test will return a +ve result 99% of the time.

If a person doesn't have the disease, the test will return a +ve result 2% of the time.

what is the probability of a person having the disease, given that they have a +ve result?

components:

D = 0.001 (1 in a 1000...)

P(+ve | D) = 0.99

P(+ve | not D) = 0.02

asked to find: P(D | +ve).

Formula (bayes theorem):

P(D | +ve) =

P(D)P(+ve | D)

-----------------------------------------------------

P(D)P(+ve | D) + P(not D)P(+ve | not D)

if you plug in the values you get P(D | +ve) = 0.0472

this is clearly too small, if the result was +ve, you'd expect a substantial amount of the +ve cohort to actually have the disease. I've checked the formula 100 times and everything seems correct.

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# Bayes theorem, answer way too small something wrong?

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