Question

Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?

Answer 1

9 / 13

Explanation:

From the question :

Let :

Hostel students = h

Day students = d

Students with A grade = a

P(h) = 60% = 0.6

P(d) = 40% = 0.4

P(hostel with A grade) ; P(A / H) = 0.3

P(day with A grade) ; P(A / D) = 0.2

The probability that a student picked at random withbA grade is an hostel student is given as :

Probability of being an hostel student gun he has A :

P(H | A) = (P(A/H) * P(H)) ÷ P(A/H) * P(H) + P(A/D) * P(D))

P(H | A) = (0.3 * 0.6) ÷ ((0.3*0.6) + (0.2*0.4))

P(H | A) = 0.18 ÷ (0.18 + 0.08)

P(H | A) = 0.18 ÷ 0.26

P(H | A) = 9 / 13