In a certain assembly plant, three machines, B1, B2, B3 make 30%, 45%, and 25%, respectively, of

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Question:

In a certain assembly plant, three machines, B1, B2, B3 make 30%, 45%, and 25%, respectively, of the products. It is known from past experience that 2%, 3%, and 2% of the products made by each machine, respectively, are defective. Now suppose that a finished product is randomly selected.

a.) What is the probability that it is defective?

b.) If a product were chosen randomly and found to be defective, what is the probability that it was made by machine B3.