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, Pittsburgh, and Toledo. 23% of the components produced come from the Buffalo factory. 41% of components come from the Pittsburgh factory, and 36% of the components come from the Toledo factory. It is known that 1.9% of the components from the Buffalo factory, 1.8% of the components from the Pittsburgh factory, and 2.6% of the components from the Toledo factory are defective. Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Toledo?

Solution

Probabilty of selecting the defective item = 0.019 x 23 + 0.018 x 41 + 0.026 x 36

probabily of seleting defective iteem from toledo = 0.026 x 36

so required probability = 0.026 x 36/(0.019 x 23 + 0.018 x 41 + 0.026 x 36) = 0.443391757