It is estimated that 5.9% of Americans have diabetes. Suppose a medical lab uses a test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it. Find the conditional probability that a randomly selected person actually has diabetes given that the lab test says they have it.

P (actually that randomly selected person has diabetes given as given by the lab) = 0.7725

Explanation:

A probability is a number, between 0 and 1, expressing the precise likelihood of an event happening.

Probability (person actually has diabetes) = 5.9%

P(lab test says that they have diabetes) = 0.0764

P (actually that randomly selected person has diabetes given as given by the lab) = 0.7725

Workings shown in the figure below.

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