Q24 of 45 Page 1

Of the students in a college, it is known that 60% reside in hostel and 40% day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain ‘A’ grade and 20% of day scholars attain ‘A’ grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an ‘A’ grade, what is the probability that the student is a hosteler?

Let P(E1) be the probability of students residing in hostel.




Let P(E2) be the probability of day scholar students.




30% of hostel students get an A grade


⇒ P (E│E1 ) = 30% = 0.3


20% of day scholar students get an A grade


By Baye’s Theorem



∴ the probability that the ‘A’ grade student chosen is a hostler is;







= 0.692


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