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Problem 4: A large firm uses three different types (A, B, and C) of raw materials...

Problem 4: A large firm uses three different types (A, B, and C) of raw materials to manufacture its product. Previous records show that 25% of the manufactured products are produced using material A, 50% using material B, and 25% using material C. If it is known that 5% of the product made with material A are defective, 2% made with material B are defective, and 5% made with C are defective.
What is the probability that a product selected at random from this firm will be defective?
If a product selected at random from this firm is found to be defective, what is the probability that it was made from material A.




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