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Baye's Theorem - Solved Problem

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A mail order company employs three stock clerks, A,B and C, who pull items from shelves and assemble them for subsequent verification and packaging. A makes a mistake in an order (gets an item wrong or the wrong quantity) one time in a hundred, B makes a mistake in an order five times in a hundred and C makes a mistake in an order three times in a hundred. If A, B and C fill respectively 30, 40 and 30 percent of all orders, what are the probabilities that

a) a mistake will be made in an order;
b) if a mistake is made in an order, it was filled by A;
c) if a mistake is made in an order, it was filled by B?

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The problem based on Baye's Theorem is solved step by step and explanation is given in such a way that the student can use this solution as a model to solve other problems of the same type.

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