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A rare disease affects 1 in 10,000 individuals in the population. A blood test for the disease is positive for 95% of people with the disease. However, 0.4% of people without the disease will also test positive.

(a) What is the likelihood that a person, selected at random from the population, has the rare disease and tests positive for it?

(b) What is the likelihood that a person, selected at random from the population, does NOT have the rare disease and tests positive for it?

(c) Given that a person (selected at random from the general population) tests positive, what is the probability that she has the disease?

(d) Now assume that the doctor knows that 1 in 100 individuals with symptom G will have the rare disease, and he only orders the test when individuals have symptom G. Given that one of the doctor's patients tests positive, what is the probability that she has the disease?

Electrical & Electronics, Engineering

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