According to the manufacturer’s specifications, your home burglar alarm has a 95% chance of going off if someone breaks into your house. During the two years you have lived there, the alarm has gone off on five different nights, each time for no apparent reason. Suppose the alarm goes off tomorrow night. What is the probability that someone is trying to break into your house? (Note: Police statistics show that the chances of any particular house in your neighborhood being burglarized on any given night are two in ten thousand.)

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