According to a sign that was posted in my apartment building, we’re going to have a fire alarm test this coming Friday.

I’ve always thought about what would happen if there was actually a real fire during the time the fire alarms were being tested, and because the sign says not to call the police (which, I’m assuming they meant to say the fire department), there would be no help arriving and the fire would go out of control.
In my curiosity, I decided to do a bit of research to find out what the chances were of that actually happening.
According to the United States Bureau of the Census, there is a projection of approximately 116,000,000 households in the United States as of 2012. According to the Emergency Preparedness Innovations Corporation, there are approximately 2,000,000 house fires reported each year. (Of course, not all of these two million fires are going to be harmful enough to injure someone, but there is an assumption that a reported fire was significant enough that it either required professional aid to extinguish, or it caused property damage that required a police report for insurance claims.)
According to this data, there is about a 1.7% chance that there will be a house fire in your place of residence in the next year.
That’s good to know, but that doesn’t really help us much for our question because the fire alarm testing is not going to last the entire year, but rather, about 10 minutes, or one-sixth of an hour. To bring the 1.7% chance per year down to scale, we’re going to divide that by 365.25 to see what the chance is of having a house fire at your place of residence on any particular day – that computation comes out to 0.00472%.
Breaking that down even further, because there are 24 hours in one day, we are going to divide 0.00472% by 24 to see what the probability of having a house fire in a one-hour time period is – that computation comes out to 0.000197%. And finally, to see what the probability of having a house fire in a given 10-minute period is, we’re going to divide our value once more by 6 to get one-sixth of an hour.
After all these computations, we can conclude that the probability of a real fire occurring during a fire alarm testing period is 0.0000328%. Finally, we’re going to divide 100% by 0.0000328% to see how many times our probability fits into 100%. This means that you would expect to see a real fire during fire alarm testing approximately once every 3,050,568 tests.
Taking this one last step further, as of 2009, the life expectancy in the United States was 79.1 years. That’s equal to 28,891.275 days, 693,390.6 hours, or 41,603,436 minutes. When we divide the number of minutes by the number of tests required to see a real fire during a test, we get about 13.64. That means that for an average person to see a real fire during a test in their life time, they would have to be at a fire alarm testing about once every 13 minutes and 38 seconds.
Fortunately, fire alarm testing tends to only happen once every few months.