Probability?

Question

A test for a disease correctly diagnoses a diseased person as having the disease with probability of 0.85. The test incorrectly diagnoses someone without the disease as having the disease with probability of 0.10. If 1% of the people in the population have the disease, what is the chance that a person from this population who tests positive for the disease actually has the disease?

Answer 1

Let A=the person has the disease and B=the person tests positive.

First, let us find the probability that a person will test positive:

P(B) = P(B|A)*P(A) + P(B|¬A)*P(¬A) = .85 * .01 + .10 * .99 = .1075

Now by Bayes' theorem, we have that:

P(A|B) = P(B|A) * P(A)/P(B) = (.85 * .01)/.1075 ≈ 0.07907

So in fact, there is only a 7.9% chance that the person actually has the disease.

Answer 2

This is a Baysian probability. If actually want to learn this topic, then look it up and figure it out. You will gain more than having someone else tell you.