Question

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 1

Given:

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

Now,

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

⇒ P(A|U₁) = 0.002

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

⇒ P(A|U₂) = 0.02

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

⇒ P(A|U₃) = 0.2

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: