Question: The Happy Valley Machine Works Company loses a shipment of its machines due to an error by one of its three executives (Harry, Sam and Mabel), but it cannot tell with certainty which executive was responsible for the error. On the basis of past performance, it is known that the probability that Harry would make such a mistake (given that he were responsible for the shipment) is 0.1, the probability that Sam would do so is 0.05 and that Mabel would do so is 0.1. If Harry is responsible for 50% of all shipments and the rest are split evenly between Mabel and Sam, what is the probability that Sam is responsible for the lost shipment?

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