The High Probability of Low Probability Events

As many of you know, I keep a pocket notebook where I jot down ideas and things I need to do and things I hear and things I read and basically just anything I want to remember for the future. I do this throughout the day whenever something comes up, and then at the end of the day, I go through the notebook, doing something with each item (adding a new item to my to do list, adding a new item to my calendar, and so on).

Every once in a while, I come across something in my notebook that I simply don’t understand or know where it came from. Usually, it’s some strange idea I had that I didn’t record well enough, or something I overheard that I didn’t source.

This happened to me a few weeks ago, and the phrase I wrote down has stuck in my head.

The high probability of low probability events

What does that mean? I’ve found myself thinking about this phrase quite a bit lately, and I’ve come to realize that it points to a pretty important phenomenon when it comes to personal finance.

This idea is probably best explained by an example, so let me spell it out for you clearly.

In a given month, the probability of, say, my car breaking down is extremely low. The probability of having a flat tire is pretty low, too. The probability of losing my job is really, really low. The probability of someone getting seriously ill in my family is very low.

I could make a giant list of unfortunate events for which the probability of each is really low.

Of course, it’s likely that at least one of the unfortunate events on that long list is going to occur this month. By simply adding up the very small probabilities of thousands of unfortunate events, the actual odds of any of those unfortunate events occurring is actually fairly large.

Let’s say there’s a 1% chance my car will break down this month. Planning ahead for that emergency alone might not be the best move, right? If that was the only emergency that would befall my life, making a bunch of financial plans around that is probably not the wisest choice.

However, at the same time, there’s a 1% chance that I could lose my job. There’s a 1% chance that someone could get really sick in my family. There’s a 1% chance of significant storm damage to my home. There’s a 1% chance of my wife losing her job. The list goes on and on, with different percentage odds and different events.

Let’s say I can make a list of 100 events, each with a 1% chance of occurring. The way you figure up odds like that is that you actually calculate the odds of each event not occurring – a 99% chance – and then you multiply that together and then subtract from 100%. It turns out that on that list of 100 unfortunate events that each have only a 1% chance of occurring, there’s actually a 40% chance that at least one of them will occur this month, and a 0.5% chance that at least two of them will occur this month.

A 1% chance of an unfortunate event isn’t really enough to worry about. A 40% chance? That’s pretty significant.

If you think about this in the context of your own life, it’s not really surprising. Think about the last few months. You can probably think of a couple of unexpected unfortunate events that occurred, right? However, the odds of each one of those events occurring is actually pretty low in the big scheme of things. It’s just that there are so many different unlikely events that could happen that the odds are that at least one of them will happen every month or two.

In other words, there’s a high probability of a low probability event occurring. We’re not talking about a specific event, but one of a large pool of unfortunate events that might occur.

Take our family, for example. In the last month, we had a tire blowout and some wind damage from a storm. Over the course of years, those individual events might happen once, or might not happen at all, but that’s true of a lot of unfortunate events. However, eventually things like this are going to happen, and we have to be ready to financially deal with them.

To me, this is a brilliant case for why we need an emergency fund. An emergency fund isn’t necessary to protect against a singular unfortunate event. Having a fund set aside for something like a blown tire alone or wind damage alone is pretty silly – those are individually low probability events. Our emergency fund came through for us this month, in fact.

An emergency fund is very useful for the high probability of low probability events, though. It’s highly likely that over some period of time there will be some kind of an unfortunate event in your life – a car breakdown, a job loss, a sick family member, an unexpected funeral in another state, a washing machine that dies and floods the basement… the list goes on and on.

The purpose of an emergency fund is to step in and help out your monthly finances when you can’t handle an unexpected expense. Some unexpected events will happen, even if the odds of each individual possible unexpected event is tiny. Ideally, many people have enough flexibility in their budget to handle some smaller unexpected events. It’s the bigger ones, or the occasional situations where unexpected events come in bunches, where the emergency fund comes in handy.

The key thing to remember is this: an individual specific unexpected event is unlikely; however, some kind of unexpected event is actually fairly likely because there are so many different specific unexpected events that could happen that the odds add up. Because you know that some kind of unexpected event is likely to occur sometime soon, it’s a good idea to prepare for it now because you’re pretty certain it’s coming.

How do you prepare for it, then? I’ve written a great guide for building an emergency fund but it boils down to just a few simple steps. All you really need to do is set up a savings account somewhere – an online bank like Ally is a good choice. Then, set up a small weekly automatic transfer from your checking account to this savings account. After it’s set up, each week a small amount of your choosing will automatically be drawn from your checking account into that emergency fund savings account. Then, whenever you have a genuine emergency that you can’t handle, just transfer the money back from your emergency fund savings into your checking. That’s it – that’s all you have to do.

How much should you transfer? Smaller but more frequent amounts are a good idea. I recommend trying out $20 a week – that adds up to $1,040 over the course of a year. Don’t worry too much about how much you should have in that emergency fund, or how much is too much, or whether you have too little. Just let the automatic transfer drip money in there and don’t worry about it.

Also, don’t rely on credit cards as your “emergency fund” because credit cards can be lost or stolen or your identity can be stolen or the credit card network may go down. A credit card is convenient, but there are many emergencies where it just doesn’t help.

The thing to remember with an emergency fund is that it’s not just $20 disappearing each week. Instead, look at that money as security against a big disaster in the future, something that will happen. A specific type of disaster is unlikely, but a disaster of some kind likely will occur at some point in the fairly near future and you’re going to want to be prepared.

The high probability of low probability events is a real thing. Plan for it. You’ll be glad you did.

Note: I did finally figure out where the phrase came from. It came from the book Triggers by Marshall Goldsmith, which I happened to be reading at the time. It was just an offhand phrase that wasn’t really connected to the main topics at all, which is why I didn’t initially remember where it came from.

Trent Hamm

Founder & Columnist

Trent Hamm founded The Simple Dollar in 2006 and still writes a daily column on personal finance. He’s the author of three books published by Simon & Schuster and Financial Times Press, has contributed to Business Insider, US News & World Report, Yahoo Finance, and Lifehacker, and his financial advice has been featured in The New York Times, TIME, Forbes, The Guardian, and elsewhere.