Question

Of the students in a college, it is known that 60% reside in hostels and 40% are day scholars (not residing in hostels). Previous year results report that 30% of all students who reside in hostels 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 resides in a hostel?

(a) 5/13

(b) 9/13

(c) 8/13

(d) None of these

Answer 1

Using Bayes' theorem, the probability that a randomly chosen A grade student resides in a hostel is calculated to be 9/13, which is option (b).

Step-by-step explanation:

To find the probability that a randomly chosen A grade student resides in a hostel, we use Bayes' theorem:

• Let H be the event that a student resides in a hostel.
• Let D be the event that a student is a day scholar.
• Let A be the event that a student attains an A grade.

Given that P(H) = 0.60, P(D) = 0.40, P(A|H) = 0.30, and P(A|D) = 0.20.

The total probability of a student getting an A grade is:

P(A) = P(A|H)P(H) + P(A|D)P(D) = (0.30)(0.60) + (0.20)(0.40) = 0.18 + 0.08 = 0.26.

The probability that a student resides in a hostel given they have an A grade is:

P(H|A) = (P(A|H)P(H)) / P(A) = (0.30)(0.60) / 0.26 = 0.18 / 0.26 = 9/13

Therefore, the probability that an A grade student resides in a hostel is 9/13.