Question: Let a random variable Y represent the diameter of a shaft and a random variable X represent the inside diameter of the housing that

Let a random variable Y represent the diameter of a shaft and

Let a random variable Y represent the diameter of a shaft and a random variable X represent the inside diameter of the housing that is intended to support the shaft. By design the shaft is to have diameter 99.5 units and the housing inside diameter 100 units. If the manufacturing process of each of the items is imperfect, so that in fact Y is uniformly distributed over the interval (98.5, 100.5) and X is uniformly distributed over (99, 101), what is the probability that a particular shaft can be successfully paired with a particular housing, when "successfully paired" is taken to mean that X-h

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