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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 48
Total: 101
Probability that A speaks truth is
4
5
. A coin is tossed. A reports that a head appears. The probability that actually there was head is
Solution:  
Let E1 : ‘coin comes up with a head’, and E2 : ‘coin comes up with a tail’
⇒P(E1)=P(E2)=
1
2

Let E : ‘A reports that a head appear’,
P(E|E1) = P (head comes up and A speaks truth) =
4
5
and P(E|E2) = P (tail comes up and A tell a lie) =1−
4
5
=
1
5

∴ Required probability
=P(E1|A)=
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)
=
4
5
×
1
2
(
4
5
×
1
2
)+(
1
5
×
1
2
)
=
4
5

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