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 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?

Solution

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