Answer :

Given:


From 400 people


Smokers and non - vegetarian are 160


Smokers and vegetarian are 100


Non - smokers and vegetarian are 140


Let us assume U1, U2, U3 and A be the events as follows:


U1 = choosing Smokers and non - vegetarian


U2 = choosing Smokers and vegetarian


U3 = choosing Non - smokers and vegetarian


A = getting special chest disease


From the problem





P(A|U1) = P(Smoker and non - vegetarian getting Chest disease)



P(A|U2) = P(Smoker and vegetarian getting chest disease)



P(A|U3) = P(Non - smoker and vegetarian getting chest disease)



Now we find


P(U1|A) = P(The selected chest diseased person is a smoker and non - vegetarian)


Using Baye’s theorem:







The required probability is .


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