Answer :


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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