Q. 265.0( 2 Votes )

Of the students in a college, it is known that 60% reside in a hostel and 40% do not reseide in hostel. Previous year results report that 30% of students residing in hostel attain A grade and 20% of ones not residing in hostel attain A grade in their annual examination. At the end of the year, one students is chosen at random from the college and he has an A grade. What is the probability that the selected student is a hosteler?

Answer :

Let us assume U1, U2, U3 and A be the events as follows:


U1 = Student residing in Hostel


U2 = Student not residing in hostel


A = Attaining A grade


From the problem




P(A|U1) = P(student in hostel attains A grade)



P(A|U2) = P(Student not in hostel attains A grade)



Now we find


P(U1|A) = P(The student who got A grade is a hosteller)


Using Baye’s theorem:







The required probabilities are .


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