1.5.2. There are 5 urns, numbered 1 to 5. Each urn contains 10 balls. Urn, has defective balls, i = 1, ..., 5. Consider the following experiment: First an urn is selected uniformly (i.e. each urn is selected with the same probability) at random and then a ball is selected uniformly at random from the selected urn. The experimenter does not know which urn was selected. (i) What is the probability that a defective ball will be selected? (ii) If we have already selected the ball and noted that it is defective, what is the probability that it came from urn 5? Generalise to urn &; & = 1,...,5.

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