question_answer 34)

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 than 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 a hostlier ? 

Answer:

Let E1 and E2 are the events of selection of a hostlier and a day scholar respectively and F = event of getting grade A             and       Required probability = P(E1/A)                   [Baye?s theorem]