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IIT JEE Advanced 2012 Paper 1
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© examsnet.com
Question : 54
Total: 60
A ship is fitted with three engines
E
1
,
E
2
and
E
3
. The engines function independently of each other with respective probabilities
1
2
,
1
4
and
1
4
. For the ship to be operational at least two of its engines must function. Let X denote the event that the ship is operational and let
X
1
,
X
2
and
X
3
denote respectively the events that the engines
E
1
,
E
2
and
E
3
are functioning. Which of the following is (are) true?
[JEE Adv 2012 P1]
P
[
X
1
C
|
X
]
=
3
16
P [Exactly two engines of the ship are functioning | X] =
7
8
P
[
X
|
X
2
]
=
5
16
P
[
X
|
X
1
]
=
7
16
Validate
Solution:
P
(
X
1
)
=
1
2
,
P
(
X
2
)
=
1
4
,
P
(
X
3
)
=
1
4
P (X) =
P
(
X
1
∩
X
2
∩
X
3
C
)
+
P
(
X
1
∩
X
2
C
∩
X
3
)
+
P
(
X
1
C
∩
X
2
∩
X
3
)
+
P
(
X
1
∩
X
2
∩
X
3
)
=
1
4
(A)
P
(
X
1
X
|
C
)
=
P
(
X
∩
X
1
C
)
P
(
X
)
=
1
32
1
4
=
1
8
(B) P[exactly two engines of the ship are functioning | X] is
7
32
1
4
=
7
8
(C)
P
(
X
X
2
)
=
5
32
1
4
=
5
8
.
(D)
P
(
X
x
1
)
=
7
32
1
2
=
7
16
.
© examsnet.com
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