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It was known that of all 60-year-old men, 9% have some type of cancer. If the...

It was known that of all 60-year-old men, 9% have some type of cancer. If the man has cancer, an x-ray will give a positive indication for cancer 80% of the time. If the guy does not have cancer, the x-ray will give a positive indication for cancer 1% of the time. If the x-ray of a 60-year-old man’s gives a positive indication for a cancer, what will be the probability that he has cancer?

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Answer #1

Probability of cancer, P(C) = 0.09

P(C') = 0.91

P(+ | C) = 0.80

P(+ | C') = 0.01

P(C | +) = [P(C)*P(+ | C)] / [P(C)*P(+ | C) + P(C')*P(+ | C')]

= [0.09*0.80] / [ 0.09*0.80 + 0.91*0.01] = 0.8878

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