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?

Question

Philoid · Accepted 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 .