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Denzel Washington, a production manager in an iron foundry in Geismar, knows that the sand used for molding iron castings is too dry 10% of the time and too wet 20% of the time. He also knows that defective castings occur 10% of the time when the sand has the correct amount moisture, 30% of the time when the sand is too dry, and 25% of the time when the sand is too wet.
(a) Suppose that one casting is selected at random from the batch just produced. What is the probability that the casting is defective?
(b) Suppose that one casting is selected at random from the batch just produced and is found to be defective. What is the probability that the sand was too dry?
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