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

Let P( H ), P( D ) and P( A ) be the probabilities that are defined below,

The probability of student selected is hostler is P( H ).

The probability of student selected is day scholar is P( D ).

The probability of grad ‘A’ student is P( A ).

The probability that the student selected is a hostler, if he has an ‘A’ grade that is P( H A ),

P( H A )= P( H )P( A H ) P( D )⋅P( A D )+P( H )⋅P( A H ) (1)

The probability of chosen student is hostler.

P( H )=60% =0.6

The probability that student gets ‘A’ grade, given that he is hostler,

P( A H )=30% =0.3

Probability of chosen student is scholar,

P( D )=40% =0.4

The probability that student gets ‘A’ grade, if day scholar,

P( A D )=20% =0.2

Put these values in equation (1),

P( H A )= ( 0.6×0.3 ) ( 0.4×0.2 )+( 0.6×0.3 ) = 0.18 0.26 = 18 26 = 9 13

Thus, the required probability is 9 13 .