Question

A manufacturing firm produces pipes in two plants I and II with daily production 1500 and 2000 pipes respectively. The

fraction of defective pipes produced by two plants I and II are 0.006 and 0.008 respectively. If a pipe selected at random

from that day’s production is found to be defective, what is the chance that it has come from plant I or plant II?
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Answer 1

Step-by-step explanation:

Let us consider the probabilities of production

P(A)=

3500

500 = 71

P(B)= 3500 1000 = 72

P(C)=

3500

2000= 74

And,

Probability of defective pipes

By plant A=P(A/E)=0.005

By plant B=P(B/E)=0.008

By plant C=P(C/E)=0.010

Now,

from Bayes theorem

Probability of defective pipe from first plant

P(E/A)=

[P(A).P(A/E)+P(B).P(B/E)+P(C).P(C/E)]

[P(A)×P(A/E)]= [71 ×0.005+ 72 ×0.008+ 73 ×0.010]

[ 71×0.005]= [ 0.005 + 72(0.008)+ 73(0.010) ]

[ 70.005]= 0.005+0.016+0.0400.005= 0.061 0.005

=

615

So, the probability is from First factory is

615

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