Question 10:- 20% of the production is done using machine A and the rest using machine B. The rate of defects using machine A is 5% and that using machine B is 3%. The probability that a randomly
selected item which is found defective has come from machine B is
a) O 0705
b) 0.24
0.34
Cannot say
Answers
Answer:
Consider the problem
Let, E
1
andE
2
be the respective events of items produced by machine A and B.
And let x be the event that the produced item was found to be defective.
Therefore,
Probability of items produced by machine A,P (E
1
)
=60%=
5
3
Probability of items produced by machine B,P (E
2
)
=40%=
5
2
And,
Probability that machine A produced defective items, P(
E
1
x
)
=2%=
100
2
Probability that machine B produced defective items, P(
E
2
x
)
=1%=
100
1
So, the probability that randomly selected items was from machine A is given by P(
x
E
1
)
Now, Apply Bayes' Theorem
P(
x
E
1
)=
P(E
1
)P(
E
1
x
)+P(E
2
)P(
E
2
x
)
P(E
1
)P(
E
1
x
)
=
5
2
×
100
1
+
5
3
×
100
2
5
3
×
100
2
=
2+5
6
=
11
6
Hence, the required probability of machine A is
11
6