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 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|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 .

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