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A large scale study conducted over a one year period has shown that break-ins at home occur about 5% of the time in the population. The study also shows home security alarms went off 3% of the time when no
one was breaking into the home. The security alarm failed to go off 2% of the time when someone was really breaking into the home.
a: What is the probability that a home has been broken into and the alarm went off?
b: What is the probability that any randomly selected alarm goes off?
c: If an alarm is going off, what is the probability that the house was broken into?
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