probability and stastics

Question

A test for a certain disease is found to be 95% accurate, meaning that it will correctly diagnose the disease in 95 out of 100 people who have the ailment. For a certain segment of the population, the incidence of the disease is 9%. If a person tests positive, find the probability that the person actually has the disease. The test is also 95% accurate for a negative result. (Note: Use Bayes Theorem)

Answer 1

suppose we have a group of 1000 people

then 0,09 x 1000 = 90 have the disease, and 1000 - 90 = 910 dont

of the 90 that have it, 0.95 x 90 = 85.5 test positive, 4.5 test negative

of the 910 who dont have it, 864.5 test negative, 45.5 test positive

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so of the 1000, 131 test positive. of these 85.5 have disease

so 85.5 / 131 = 0.65