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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 85
Total: 101
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Solution:  
Let E1 = Selected person is a male
E2 = Selected person is a female
and A = Selected person is grey haired.
∴P(E1)=P(E2)=
1
2

P(A|E1)=
5
100
=
1
20
 & P(A|E2)=
0.25
100
=
1
400

∴ Required probability =P(E1|A)
=
P(E1).P(A|E1)
P(E1).P(A|E1)+P(E2).P(A|E2)

=
1
2
×
1
20
(
1
2
)(
1
20
)+(
1
2
)(
1
400
)
=
20
21
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