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Probability
Oswaal
CBSE
Grade 12

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 a hostelier?

Step-by-Step Solution

Key Concept: Let E1: hostelier (0.60), E2: day scholar (0.40). A: gets A grade. P(A|E1) = 0.30, P(A|E2) = 0.20. By Bayes Theorem: P(E1|A) = (0.60 * 0.30) / (0.60*0.30 + 0.40*0.20) = 0.18 / (0.18 + 0.08) = 0.18 / 0.26 = 9/13.
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Correct Answer:
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