Applied Probabilities Made Simple

In this article the author shows why "prepping" (stockpiling food, firearms, and ammunition) makes mathematical sense:

I am not a prepper. But I know a few. Some of the ones I do know are smart. They may not be doing as deep an analysis as I present here, on a mathematical level, but the smart ones are definitely doing it at a subconscious level. If you want to understand the perspectives of others, as everyone in my opinion should strive to do, then you would do well to read to the end of this article. To get where we’re going, we will need to discuss the general framework of disaster mathematics...

We don’t buy houses in the floodplain if we can help it, because we are risk averse, even though the chance of it flooding in any given year is only 1%. Why? We will live in the house longer than one year. Over the 30-year life of the mortgage, the chance the house floods at least once vastly exceeds 1%, because every year is another roll of the dice. It’s not cumulative, though. The mathematics for back-calculating the odds is called a Bernoulli Process. Here’s what the math looks like...

Let’s quickly step through this. The chance of flooding, P(F), is 1%, or 0.01. The chance of not flooding, which we notate P(F’), is 100%-1%, or 99%, or 0.99. To see the chance you don’t flood two years in a row, you would have to “not-flood” the first year, and then “not-flood” the second year, so you multiply the two probabilities together, and get 0.9801. The chance of “not-flooding” 30 years in a row is calculated by multiplying the chance of not flooding with itself, over and over, 30 times, which is a power relationship. P(F’)³⁰. That’s 0.7397 chance of 30 consecutive years of no flood, which means a 26% chance of at least one flood.

And then on to revolution:

While we don’t have any good sources of data on how often zombies take over the world, we definitely have good sources of data on when the group of people on the piece of dirt we currently call the USA attempt to overthrow the ruling government. It’s happened twice since colonization. The first one, the American Revolution, succeeded. The second one, the Civil War, failed. But they are both qualifying events. Now we can do math.

Stepping through this, the average year for colony establishment is 1678, which is 340 years ago. Two qualifying events in 340 years is a 0.5882% annual chance of nationwide violent revolution against the ruling government. Do the same math as we did above with the floodplains, in precisely the same way, and we see a 37% chance that any American of average life expectancy will experience at least one nationwide violent revolution.

This is a bigger chance than your floodplain-bound home getting flooded out during your mortgage...

Two instances in 340 years is not a great data pool to work with, I will grant, but if you take a grab sample of other countries around the world you’ll see this could be much worse. Since our 1678 benchmark, Russia has had a two world wars, a civil war, a revolution, and at least half a dozen uprisings, depending on how you want to count them. Depending on when you start the clock, France had a 30-year war, a 7-year war, a particularly nasty revolution, a counter-revolution, this Napoleon thing, and a couple of World Wars tacked on the end. China, North Korea, Vietnam, and basically most of the Pacific Rim has had some flavor of violent revolution in the last 100 years, sometimes more than one. Africa is … hard to even conceive where to start and end the data points. Most Central and South American countries have had significant qualifying events in the time span. And honestly, if we were to widen our analysis to not only include nationwide violent civil wars, but also instances of slavery, internment, and taking of native lands, our own numbers go way up.

Practical/applied probability.  It's very interesting.  Go read the whole thing.