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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 38
Total: 101
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 hostlier ?
Solution:  
Let E1 : ‘A student is hostlier’ and E2 : ‘A student is day scholar’
⇒P(E1)=
60
100
=
3
5
 and P(E2)=
40
100
=
2
5

Let E : ‘student attains A grade’ then P(E|E1)=
30
100
=
3
10
 and P(E|E2)=
20
100
=
2
10

Hence, required probability P(E1|E) =
P(E|E1)P(E1)
P(E|E1)P(E1)+P(E|E2)P(E2)

=
3
10
×
3
5
(
3
10
×
3
5
)(
2
10
×
2
5
)
=
9
13
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