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UPSC NDA Math Model Paper 8
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© examsnet.com
Question : 40
Total: 120
A person speaks truth 3 out of 4 times. A dice was rolled in his presence and he told that the number was 2, what is the possibility that the number is actually 2?
1
6
3
8
1
4
1
8
Validate
Solution:
In the given case
Case A: The person is reported 2
Case
E
1
:
The number on dice is 2
∴
P
(
E
1
)
=
1
6
Case
E
2
:
The number on dice is
n
o
t
2
∴
P
(
E
2
)
=
5
6
Man reported 2 and 2 appears, i.e., man speaking true
⇒
P
(
A
|
E
1
)
=
3
4
Man reported 2 and 2 do not appears, i.e., man speaking false
⇒
P
(
A
|
E
2
)
=
1
4
For 2 actually appeared
P
(
E
1
|
A
)
=
P
(
A
|
E
1
)
P
(
E
1
)
P
(
A
|
E
1
)
P
(
E
1
)
+
P
(
A
|
E
2
)
P
(
E
2
)
⇒
P
(
E
1
|
A
)
=
3
4
×
1
6
3
4
×
1
6
+
1
4
×
5
6
⇒
P
(
E
1
|
A
)
=
3
8
© examsnet.com
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