Question

Your next-door neighbor has a rather old and temperamental burglar alarm. if someone breaks into his house, the probability of the alarm sounding is 0.95. in the last two years, though, it has gone off on five different nights, each time for no apparent reason. police records show that the chances of a home being burglarized in your community on any given night are 2 in 10,000. if your neighbor's alarm goes off tomorrow night, what is the probability that his house is being broken into

Answer 1

The probability is 2 in 10,000, which can be reduced to 1 in 5,000. The burglar alarm has gone off 5 times in the last two years for no reason, and therefore the fact that it is sounding does not affect the actual probability of a break-in.