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1. Bike owners on campus sometimes buy locks to reduce the chance of theft. Suppose that the probability of theft without a lock is .25, and the probability with a lock is .05. If the value of the bike is $200, and the cost of the lock is $25, is it worthwhile to buy the lock?
2. Now, suppose the college police increase their patrols, thereby lowering the probability of theft to .10 with no lock, and 0 with a lock. However, students are assessed an extra $10 each to cover the cost. Is it now efficient to buy the lock?
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