Question

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars. Previous year result report that 30% of all student who reside in hostel attain, A grade and 20% of day schloars 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 on A grade, what is the probability that the student is a hostlier?

Answer 1

Let E₁ : Event that students reside in hostel and E₂ : Event that students do not reside in hostel 

∴ Probability of students reside in hostel

P(E₁) = 60%

= 60/100 = 0.6

Probability that students do not reside in hostel

P(E₂) = 40% = 40/100 = 0.4

Probability of students securing grade A who reside in hostel

= P(A/E₁) = 30%

= 30/100 = 0.3

Probability of students who do not reside in hostel but. secure grade A

= P(A/E₂) = 20%

= 20/100 = 0.2

∴ Probability that student securing graded is a hostelier = P(E₁/A)

Hence, required probability : 9/13