Q. 195.0( 1 Vote )

In a group of 400 people, 160 are smokers and non - vegetarian, 100 are smokers and vegetarian and the remaining are non - smokers and vegetarian. The probabilities of getting a special chest disease are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the disease. What is the probability that the selected person is a smoker and non - vegetarian?

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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses