Q24 of 26 Page 1

40% students of a college reside in hostel and the remaining reside outside. At the end of year, 50% of the hosteliers got A grade while from outside students, only 30% got A grade in the examination. At the end of year, a student of the college was chosen at random and was found to get A grade. What is the probability that the selected student was a hostelier?

Let events E1, E2be the following:

E1 be the event that the student is a hosteller


and E2 be the event that the student reside outside


So,


Now, Let E be the event that the chosen student gets A grade


P(E|E1) is the probability that the student getting A grade is hosteller


P(E|E2) the probability that the student getting A grade is an outside student



We use Bayes’ theorem to find the probability that a randomly chosen student is a hosteller, given that he got A grade, given by P(E1|E)


∴







[Divide by 2 both numerator and denominator]


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