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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 46
Total: 101
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A ?
Solution:  
Let E1 : ‘Item is produced by machine A’, E2 : ‘Item is produced bymachine B’ and E3 : ‘Item is produced by machine C’,
⇒P(E1)=
50
100
, P(E2)=
30
100
 and P(E2)=
20
100

Let A : ‘Item chosen is found to be defective’,
then P(A|E1)=
1
100
, P(A|E2)=
5
100
 and P(A|E3)=
7
100

Hence, required probability,
=P(E1|A)=
P(A|E1)P(E1)
P(A|E1)P(E1)+P(A|E2)P(E2)+P(A|E3)P(E3)
=
1
100
×
50
100
(
1
100
×
50
100
)+(
5
100
×
30
100
)+(
7
100
×
20
100
)
=
5
34
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