In bayesian analysis, can you answer this question for me?? Os illness, a medica

Question

In bayesian analysis, can you answer this question for me?? Os illness, a medical screening of the population is proposed. The probability that the test correctly identifies someone with the illness as positive is 0.99, and the probability that the test correctly identifies someone without the illness as negative is 0.95, the incidence of the illness in the general population is 0.0001. You take the test, and the result is positive. What is the probability that you have the illness? medical procedure has been shown to be effective in the early detcction of an

Explanation / Answer

P(I) = 0.0001 and P(I') = 0.9999
P(P|I) = 0.99 and P(P|I') = 0.01
P(P'|I') = 0.95

Required probability, P(I|P) = P(P|I)*P(I) / (P(P|I)*P(I) + P(P|I')*P(I'))

= 0.99*0.0001 / (0.99*0.0001 + 0.01*0.9999)

= 0.0098

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