What is the probability P(P) that you test positive? What is the probability P(W|P) that you don't have the disease, given that you tested positive? What is the probability P(D and P) that you have the disease and test positive?
In a population, 5% of the people have a very serious disease. A sreening test has been designed to screen for the disease. Of those people that have the disease, 1% will test negative. Of the people that don't have the disease, 5% will test positive Let D be the event that you have the disease Let W be the event that you are well (you don't have the disease). Let P be the event that you test positve. Let N be the event that you test negative. With this information, we know the following probabilities:
P(D) = 0.05
P(N|D) = 0.01
P(P|W) = 0.05
What is the probability P(P) that you test positive?
What is the probability P(W|P) that you don't have the disease, given that you tested positive?
What is the probability P(D and P) that you have the disease and test positive?
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