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Probability Ncert Solutions Maths class 12th Maths Class 12th Probability

37. 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 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 hosteller?

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alok kumar singh | Contributor-Level 10

4 months ago

37. Let, $E_{1}$ :event that the student in hostel

$E_{2}$ : event that the student is day scholar

$A$ : be the event of the chosen student get grade $A$

$P (E_{1}) = 60 % = \frac{60}{100} = 0.6$

$P (E_{2}) = 40 % = \frac{40}{100} = 0.4$

$P (A / E_{1}) = P$ (student getting an $A$ grade is hostler) $= 30 %$ $= \frac{30}{100} = 0.3$

$P (A / E_{2}) = P$ ( student getting an $A$ grade is a day scholar) $= 20 % = \frac{20}{100} = 0.2$

Then, by Baye’s theorem,

$P (E_{1} / A) = \frac{P (E_{1}) . P (A / E_{1})}{P (E_{1}) . P (A / E_{1}) + P (E_{2}) . P (A / E_{2})}$

$= \frac{0.6 \times 0.3}{0.6 \times 0.3 + 0.4 \times 0.2} = \frac{0.18}{0.26} = \frac{18}{26} = \frac{9}{13}$

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