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# Suppose that when a machine is adjusted properly 50% of the items produced by it are of high quality and the other 50% are of medium quality.

Suppose that when a machine is adjusted properly 50% of the items produced by it are of high quality and the other 50% are of medium quality. Suppose however, that the machine is improperly adjusted during 10% of the time and that, under these conditions, 25% of the items produced by it are of high quality and 75% are of medium quality.(a) suppose that 5 items by the machine at a cetain time are selected at random and inspected. If four of these items are of high quality and one item is of medium quality, what is the probability that the machines was adjusted at that time?(b) suppose that one additional item, which was produced by the machine at the same time as the other five items is selected and found to be of medium quality. What is the new posterior probability that the machine was properly adjusted?