Assume there are three machines I, II, and III in a semiconductor manufacturing facility that make chips. They manufacture, respectively, 20, 30, and 50 percent of the total semiconductor chips there. Of their outputs, respectively, 5, 4, and 2 percent of the chips are defective. A chip is drawn randomly from the combined output of the three machines. (1) What is the probability that this chip is defective? (2) Given that this chip is found defective, what is the probability that it was manufactured by machine I?

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A: Given , P( A ) = 0.41 ,  P( defective | A ) = 0.01 P( B ) = 0.38 ,  P( defective | B ) = 0.02 P( C )…

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A: D = defective  b1=0.30 b2 0.45 b3 =0.25 db1 =0.02 d/b2=0.03 d/b3=0.02

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