SOLUTION: The proportion of people in a given community who have a certain disease is 0.004. A test is available to diagnose the disease. If a person has the disease, the probability that th

Question 1019448: The proportion of people in a given community who have a certain disease is 0.004. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.05. If a person tests positive, what is the probability that the person actually has the disease?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Gather all the info available:
p(disease) = .004 (==> p(nodisease) = 0.996)
p(positive|disease) = 0.95
p(positive|nodisease) = 0.05
The problem is to find p(disease|positive).
Now p(disease|positive) = p(disease AND positive)/p(positive)
=(p(positive|disease)*p(disease))/(p(positive|disease)*p(disease) + p(positive|nodisease)*p(nodisease))
=(0.95*0.004)/(0.95*0.004 + 0.05*0.996)=0.0038/(0.0038+0.0498) = 0.0038/0.0536
=0.071, to 3 decimal places.

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