Question

Of the students in a college, it is known that 60% reside in hostel and 40% are 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 hostler?

Answer 1

E₁, E₂ and A represent the following:

E₁ = students living in hostels,

E₂ = Students not residing in hostels

and A = students who get A-grades

Now P(E₁) = `60/100 = 3/5`, P(E₂) = `40/100 = 2/5`

P(A|E₁) = `30/100 = 3/10`, P(A|E₂) = `20/100 = 2/10`

By Bayes' theorem

P(E₁|A) = `(P(A|E_1) P(E_1))/(P(A|E_1)P(E_1) + P(A|E_2)P(E_2))`

`= (3/10 xx 3/5)/((3/10 xx 3/5) + (2/10 xx 2/5))`

`= 9/ (9 + 4)`

`= 9/13`