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An item is manufactured by three machine...

An item is manufactured by three machines A, B and C. Out of the total member of items manufactured during a specified period, 50% are manufactured on A, 30% on B and 20% on C. 2% of the items produced on A and 2% of items produced on B are defective and 3% of these produced on C are defective. All the items are stored at one godown. One item is drawn at random and is found to be defective. What is the probability that it was manufactured on machine A?

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To solve the problem, we will use Bayes' theorem. Let's break down the solution step by step. ### Step 1: Define Events Let: - \( E_1 \): Event that the item is manufactured by machine A. - \( E_2 \): Event that the item is manufactured by machine B. - \( E_3 \): Event that the item is manufactured by machine C. - \( E \): Event that the item is defective. ...
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