A company that produces a particular machine component has 3 factories, one each

Question

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 the 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?

Explanation / Answer

Dear Student Thank you for using Chegg !! Given the machine component is produced in 3 factories Let the total number of components produced in 3 factories combined be X Defective Components 1) Components produced in Buffalo = 0.23X 0.00437X 2) Components produced in Pittsburg = 0.41X 0.00738X 3) Components produced in Toledo = 0.36X 0.00936X Total Number of defective Coponents = 0.02111X Probability that a defective component is made in Toledo = Defective Components in toledo / Total Number of Defective Components = 0.00936X / 0.02111X = 0.443392 Solution

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