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In a factory which manufactures bolts, m...

In a factory which manufactures bolts, machines A. B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B?

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To solve the problem step by step, we will use Bayes' theorem to find the probability that a defective bolt was manufactured by machine B. ### Step 1: Define the Events Let: - \( A \): The event that the bolt is manufactured by machine A. - \( B \): The event that the bolt is manufactured by machine B. - \( C \): The event that the bolt is manufactured by machine C. - \( D \): The event that the bolt is defective. ...
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