A company that produces a particular machine component has 3

A company that produces a particular machine component has 3 factories, one each in Buffalo, Dayton, and Pittsburgh. 29% of the components produced come from the Buffalo factory, 32% of the components come from the Dayton factory, and 39% of the components come from the Pittsburgh factory. It is known that 1.9% of the components from the Buffalo factory, 1.4% of the components from the Dayton factory, and 1.2% of the components from the Pittsburgh factory are defective. Given that a component is selected at random and is found not to be defective, what is the probability that the component was made in Dayton?

Solution

This is a classic example of Bayes theorem.

The required probability will be :   P ( ND) * P(D) / ( Total probability of it being Non-defective)

Thus,

the total probability that the product will be non-defective =

= (0.29 * 98.1% ) + (0.32 * 98.6%) + (0.39 * 98.8%)

Probability of a non-defective product from dayton = 0.32 * 98.6%

Thus,

Required probability

= ( 0.32 * 98.6% ) / (0.29 * 98.1% ) + (0.32 * 98.6%) + (0.39 * 98.8%)

= 32.02%

Thus, if product is found to be non-defective, 32.02% chances are that it is from Dayton.

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