Answer :

Let events E_{1}, E_{2}be the following:

E_{1} be the event that the student is a hosteller

and E_{2} be the event that the student reside outside

So,

Now, Let E be the event that the chosen student gets A grade

P(E|E_{1}) is the probability that the student getting A grade is hosteller

P(E|E_{2}) the probability that the student getting A grade is an outside student

We use Bayes’ theorem to find the probability that a randomly chosen student is a hosteller, given that he got A grade, given by P(E_{1}|E)

**∴**

[Divide by 2 both numerator and denominator]

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