Ex 13.3, 3 - Of students in a college, 60% reside in hostel - Ex 13.3

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  1. Chapter 13 Class 12 Probability
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Transcript

Ex 13.3, 3 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 hostler? Let H : student selected is a hostler D : student selected is a day scholar A : student has an ‘A’ grade We need to find the Probability that the student selected is a hostler, if he has an ‘A’ grade. i.e. P(H|A) So, P(H|A) = P(H) . P(A|H) ﷮P(D) . P(A|D) + P(H) . P(A|H)﷯ Putting values in formula, P(H|A) = 0. 6 × 0. 3﷮0. 4 × 0. 2 + 0. 6 × 0. 3﷯ = 0 .18﷮0. 08 + 0. 18﷯ = 0. 18﷮0. 26﷯ = 18﷮26﷯ = 9﷮13﷯ Therefore, required probability is 𝟗﷮𝟏𝟑﷯

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