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A test kit for a certain disease whose base risk is at 0.005 is under development....

A test kit for a certain disease whose base risk is at 0.005 is under development. The kit is expected to yield the same true-positive rate as its true-negative rate, which both are referred to as accuracy rate (call it ?). Define an authentic positive case as an incidence where given a patient tested positive, they actually have the disease.

a. If the accuracy rate of the kit is 0.95, what is the probability for an authentic positive case?

b. Find the minimum value of ? such that the probability for an authentic positive case is at least 0.95.

Math   Statistics-And-Probability   
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