Q. 395.0( 1 Vote )

There are three categories of students in a class of 60 students: A: Very hardworking; B: Regular but not so hardworking; C: Careless and irregular 10 students are in category A, 30 in category B and rest in category C. It is found that the probability of students of category A, unable to get good marks in the final year examination is 0.002, of category B it is 0.02 and of category C, this probability is 0.20. A student selected at random was found to be one who could not get good marks in the examination. Find the probability that this student is of category C.

Answer :


10 students are in category A

30 students are in category B

20 students are in category C

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

U1 = Choosing student from category A

U2 = choosing student from category B

U3 = choosing student from category C

A = Not getting good marks in final examination


P(A|U1) = P(student not getting good marks from category A)

P(A|U2) = P(student not getting good marks from category B)

P(A|U3) = P(student not getting good marks from category C)

Now we find

P(U3|A) = P(The student is from category C given that he didn’t get good marks in final examination)

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