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Question

A company has two plants to manufacture scooters. Plant-1 manufactures 70 of the scooters and plant-2 manufactures 30%. At plant-1, 30% of the scooters are rated of standard quality and at plant-2, 90% of the scooters are rated as standard quality. A scooter is chosen at random and is found to be of standard quality. Find the probability that it has come from plant 2.

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Solution

Consider the problem

Let,

E1 is the plant I manufactured scooter

E2 the plant II manufactured scooter

And, A is scooter of standard quality

Then,

P(E1)=70100P(E2)=30100

And,

P(AE1)=30100P(AE2)=90100

Now, apply Bayes' Theorem

P(E2A)=P(E2)P(AE2)P(E1)P(AE1)+P(E2)P(AE2)

=(30100×90100)(70100×30100)+(30100×90100)=2721+27=2748

Hence, The probality that the standard quality has come out from Plant II is 2748

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