# 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?

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

U1 = Student residing in Hostel

U2 = Student not residing in hostel

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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