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Probability Practice Test 2
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© examsnet.com
Question : 36
Total: 37
In a factory where toys are manufactured, machines A, B and C produce 25%, 35% and 40% of the total toys, respectively. Of their output, 5%, 4% and 2% respectively, are defective toys. If a toy drawn at random is found to be defective, what is the probability that it is manufactured by Machine B?
17
69
28
69
35
69
None of these
Validate
Solution:
Let A = Event of manufacturing on Machine A
B = Event of manufacturing on Machine B
C = Event of manufacturing on Machine C
D = Event of manufacturing on defective item
∴ P(A) = P(B) = P(C) =
1
3
P
(
D
A
)
=
5
25
,
P
(
D
B
)
=
4
35
,
P
(
D
C
)
=
2
40
Now using Bayes’ theorem,
P
(
B
D
)
=
P
(
D
B
)
.
P
(
B
)
P
(
D
A
)
.
P
(
A
)
+
P
(
D
B
)
.
P
(
B
)
+
P
(
D
C
)
.
P
(
C
)
=
4
35
×
1
3
5
25
×
1
3
+
4
35
×
1
3
+
2
40
×
1
3
=
16
51
© examsnet.com
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