A screening test for a certain disease is used in a large population of people of whom 1 in 1000 actually have the disease. Suppose that the false positive rate is 1% and the false negative rate is 0.5%. Thus a person who has the disease tests positive for it 99.5% of the time, and a person who does not have the disease tests negative for it 99% of the time. (a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (b) What is the probability that a randomly chosen person who tests negative for the disease actually has the disease? Show transcribed image text A screening test for a certain disease is used in a large population of people of whom 1 in 1000 actually have the disease. Suppose that the false positive rate is 1% and the false negative rate is 0.5%. Thus a person who has the disease tests positive for it 99.5% of the time, and a person who does not have the disease tests negative for it 99% of the time. (a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (b) What is the probability that a randomly chosen person who tests negative for the disease actually has the disease?
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