Q. 304.7( 6 Votes )

# 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 :

Given:

10 students are in category A

30 students are in category B

20 students are in category C

Let us assume U_{1}, U_{2}, U_{3} and A be the events as follows:

U_{1} = Choosing student from category A

U_{2} = choosing student from category B

U_{3} = choosing student from category C

A = Not getting good marks in final examination

Now,

⇒

⇒

⇒

⇒ P(A|U_{1}) = P(student not getting good marks from category A)

⇒

⇒ P(A|U_{2}) = P(student not getting good marks from category B)

⇒

⇒ P(A|U_{3}) = P(student not getting good marks from category C)

⇒

Now we find

P(U_{3}|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 .

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