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KEAM 2023 Math Solved Paper
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© examsnet.com
Question : 41
Total: 120
An electric bulb manufacturing company manufactures three types of electric bulbs
A
,
B
and
C
. In a room containing these three types of electric bulbs, it is known that
6
%
of type
A
electric bulbs are defective,
4
%
of type
B
electric bulbs are defective and
2
%
of type C electric bulbs are defective. An electric bulb is selected at random from a lot containing 50 type
A
electric bulbs, 30 type
B
electric bulbs and 20 type
C
electric bulbs. The selected electric bulb is found to be defective. Then the probability that the selected electric bulb was type
A
is
2
23
23
500
12
23
15
23
6
115
Validate
Solution:
Applying Bayes' theorem
P
[
E
1
∕
A
]
=
P
[
E
1
]
[
A
∕
E
1
]
3
Σ
i
=
1
P
[
E
i
]
P
[
A
∕
E
i
]
=
50
100
⋅
6
100
50
⋅
6
100
⋅
100
+
30
⋅
4
100
⋅
100
+
20
⋅
2
100
⋅
100
=
15
23
© examsnet.com
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