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 anA grade, what is the probability that the student is a hostlier?​

Answer 1

Let A denote A−grade.

H denote from hostel.

D denote day scholar.

P(A/H)=0.3 and P(A/D)=0.2

P(H)=0.6 and P(D)=0.4

P(H/A)=

P(A/H)×P(H)+P(A/D)×P(D)

P(A/H)×P(H)

P(H/A)= 0.3×0.6+0.2×0.40.3×0.6

P(H/A)= 0.18+0.08 .0.18

P(H/A)= 26/18

= 13/9

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