Bayes Theory- The proportion of people in a given community who have a certain d

Question

Bayes Theory- The proportion of people in a given community who have a certain disease is 0.005. 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 0.99. If a person does not have the disease, the probability that the test will produce a positive signal is 0.01. If a person tests positive, what is the probability that the person actually has the disease? Show work. Show variable definitions and the tree diagram completely filled in.

Explanation / Answer

If a person tests positive then the probability that the person actually has the disease is 0.00495.

Event Prior Probability Conditional Probability Joint Probability Revised Probability Disease 0.005 0.99 0.00495 0.3322 Do not have disease 0.995 0.01 0.00995 0.6678 0.0149 1

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