7·Suppose a 60-year-old man who has never smoked cigarettes presents to a physic

Question

7·Suppose a 60-year-old man who has never smoked cigarettes presents to a physician th symptoms of a chronic cough and occasional breath-lessness. The physician becomes concerned and orders the patient admitted to the hospital for a lung biopsy Suppose the results of the lung biopsy are consistent either with lung cancer or with sarcoidosis, nonfatal lung disease. In this case, A = {chronic cough, results of lung biopsy) Disease state, (BL-normal, B2= lung cancer, B,-sarcoidosis) Suppose that Pr(AB) :001, Pr(A/B) = .9, Pr (A/B3)-.009 and that in 60-year-old. never-smoking men, Pr(Bi) = .99, Pr (B2)-.001, Pr (B) = .009 The first set of probabilities Pr(A/B.) could be obtained from clinical experience with the previous diseases, whereas the latter set of probabilities Pr(B,) woud have to be obtained from age-, sex-, and smoking-specific prevalence rate for the diseases in question. The interesting question now becomes what are the probabilities Pr(Bi/A) of the three disease states given the previous symptoms?

Explanation / Answer

here probability of A =P(A)=P(B1)*P(A|B1)+P(B2)*P(A|B2)+P(B3)*P(A|B3)

=0.99*0.001+0.001*0.9+0.009*0.009 =0.001971

hence P(B1|A) =P(B1)*P(A|B1)/P(A) =0.99*0.001/0.00171 =0.5023

P(B2|A)=P(B2)*P(A|B2)/P(A)=0.001*0.9/0.001971 =0.4566

P(B3|A)=P(B3)*P(A|B3)/P(A)=0.009*0.009/0.001971 =0.0411

please revert for any explanation

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