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5.86 Alice, Bill, and Charley( who can be labeled A, B, and C) are employers of...

5.86 Alice, Bill, and Charley( who can be labeled A, B, and C) are employers of a fast-food restaurant, taking orders from customers at a counter. From prior observation, we know that A makes mistakes 1 time in 100, B makes mistakes 3 times in 100, and C makes mistakes 5 times in 100. A, B, and C take 50%, 30%, and 20% of the orders. If the manager finds that a mistake, M, has been made in a certain order, what are probabilities that the order was filled by A, B, and C?

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