I was thinking about probability the other day. Why? I heard a rather remarkable story. A man who was struck by lightning won the lottery…and his daughter was also struck by lightning. The odds of such a thing occurring? 1 in 2.6 trillion. Let me put that in perspective for you:

1 in 2,600,000,000,000.

Now why is this relevant? Because he beat the odds. Incredibly long odds. Odds that are so long it’s really hard to compare it to anything else. Which made me think about what it really means for something to be “improbable.”

A lot of people take improbable to be the equivalent of impossible when we’re talking about 1 in 2.6 trillion. Clearly, though, something being improbable–even incredibly, remotely improbable–doesn’t preclude its possibility. It seemed, as I pondered this, that improbability might not even make something more unlikely.

Given a system as large as the universe and a large enough span of time, one would think that incredibly “rare” events, like this man and his daughter both being struck by lightning and then winning the lottery, wouldn’t really be that rare. That given a large enough stage and enough time, even very unlikely things would play out.

Imagine that you and your daughter have both survived being struck by lightning (let’s hope this doesn’t really happen). To celebrate the fact, you decide to buy a lottery ticket because, hey, you’re feeling lucky after surviving that! Now imagine that you’re about to buy the ticket, and your friend who accompanied you (who apparently is a master statistician) points out, “Hey, do you realize that if you bought that ticket your odds of winning would be 1 in 2.6 trillion?” What would you think? It might not stop you from buying the ticket on a whim, but you’d probably think you have less than a snowball’s chance in hell of winning.

And yet, someone did exactly that.

And it didn’t take a billion years. He didn’t need to buy 2.6 trillion lottery tickets to make it happen. It took a very very very short amount of time on a cosmic scale to occur. So I asked myself, well does improbability even mean anything, then? Can amazing, mind-boggling things that seem to happen against all odds actually be commonplace throughout the universe? What if rare events and amazing coincidences happen all the time? To take this to a level worthy of Christopher Nolan’s *Inception*, there’s nothing that says very improbable things can’t happen often–they just *probably* won’t. In other words, the odds of the everything being favorable for rare things to happen frequently are slim, but not nil. It could very well be that things have happened to have occurred in a way as to allow improbable things to occur frequently.

Of course it could also very well be that I don’t understand math that well, and that these random thoughts I’ve had are totally wrong. In fact, that seems highly probable.

The truly remarkable day would be the day where nothing remarkable happened.

It makes them more rare, but assuming one “chance” is one second, then you’re not likely to win the lottery in your life with a chance of 2.6e12, but with 317 million, it’s bound to happen (and, in fact, has to. That’s the lottery’s fault, though). This kind of reminds me of that guy who got struck by lightning 5 or 6 times in his life, then his grave got struck by lightning.

There are a few things that I want to say here, but let me start by the first saying that these calculated odds, in this case are meaningless because these things are totally unrelated and you can do the math and combine them, but it really doesn’t make sense. Let me explain. Let’s look at a situation where it does make sense. Let’s say I want to draw all the aces by randomly picking them from a deck of cards. For the first ace I have a 1/13 chance. For the next one I have a 1/17 chance, and then a 1/25 chance, and then finally, I have a 1/49 chance. If I do it (assuming a randomly shuffled deck) then I have done something that had a 1 and (13x17x25x49) 270725 of happening. This is pretty good, and this statistical chance of it happening makes sense, because it is all related. But what they are doing here is a little bit of a magic trick. It would be like if I took a number of improbably events in my life like: I found a $100 bill on the sidewalk, I got the highest possible hand in cribbage, my watch stopped working at the exact time I was born, and I happened to win a radio contest where 100,000 people entered…well the list goes on, and if I could calculate the odds of each of those and then multiply them together I could probably get to 2.6 trillion eventually myself. But it really wouldn’t mean shit.

That being said, such odds are often calculated based on averages that are statistically valid either. Perhaps the behavior of these two people were that they were outdoors a lot during thunderstorms, and lived in areas that got thunderstorms frequently. Their odds of being hit by lightning are significantly greater. And if you do get hit by lightning, your chances of surviving a lightning strike are actually surprisingly good. I think only about 1/3rd of the people die from lightning strikes once hit. Anyway, the calculation that is used for the odds of people being hit by lightning is based like on total strikes over the population of the U.S. or something, so it is severely skewed towards the odds being really low of being hit, when in fact the odds are higher in some areas than others.

And Celia and your ruminations quite right. Low probability events happen all the time in a vast universe that has been around for a long time. On earth there are 7 billion people and so 1 and billion events which make for quite remarkable stories can be told 7 times a day. The Dawkins “Unweaving the Rainbow” has an excellent discussion about this. The average persons inability to understand probabilities is a big problem. Mostly the disconnect is born out of the fact that are brains from an evolution standpoint are stone age when we lived in groups of 200, and so we would essentially never come across low probability events. In our large population, civilized world, with the internet connecting everybody, these low probability events happen all the time and we think it represents some sort of pattern, or has meaning. It is remarkable of course, but that’s all it is. 🙂

So in short, I was correct in stating that I understand the math incorrectly 😛

While I certainly wouldn’t argue that the probability of being struck by lightning somehow affects the probability of winning the lottery, does not the notion that “rare” things can happen in the close temporal proximity mean anything?

Re-reading your comment, I guess I did sort of agree with the idea that improbability is meaningless. If something happens that it’s no longer improbable. The linguistics of this topic can be highly confusing lol.

It is the improbable that creationists like to mislabel as the impossible. The odds of life beginning on its own seem ver long. But as this story shows it need only happen once. Evolution took over soon after.

Now all we have to do is explain that again, for the umpteen thousandth time…

I really thought that was where you were headed…

I stopped short because I wasn’t sure if my ramblings were making any sense lol. But you’re right, something need only happen once to prove that it’s not only possible but likely.

Hey Ryan, let me just post another general comment to reply to yours as it will be easier than replying to each one individually. lol

First of all I think you actually have a better intuitive understanding about probabilities than most, in fact I find those that are secular and good critical thinkers naturally think about probability in a more meaningful way. Because really understanding probabilities is really thinking about the size of possible outcomes properly and you seem to do that.

I don’t mean to say these rare probabilities are meaningless in an absolute sense, as I said we can still appreciate them for how rare they are, but only that we A) shouldn’t be surprised that they happen relatively frequently in todays world with many people B) they don’t have any meaning beyond that it was an improbable event and that it was cool that it happened. And I think it is important that to really appreciate the odds for something that we choose events that are related, otherwise the probabilities should be considered discrete events and the probabilities should be appreciated separately. Winning the lottery…awesome…surviving a lightning strike, maybe not so improbable.

If you want to lump unrelated events together, I mean when you think about it, it’s pretty remarkable that any of us are here. I could try to calculate the odds that my wife and I met, and would probably find that this was a rare event when I think of all the decisions that had to happen for us to meet. Then I could even go back and think about the fact that the odds of me existing depend on how my parents met and what the probability would be that they met. And we can multiply all those odds together and probability reach a trillion once again pretty easily. And I think we could be equally amazed, but, and this is just opinion, maybe we shouldn’t be because they are unrelated events. Perhaps the only relevant point is that both my wife and I were in Laramie. I spent 4 years there and was a social person and over time I am going to meet a lot of people and probably gravitate towards those who are earth scientists like myself so meeting a single girl in geology wasn’t that surprising.

The odds are extremely challenging to truly calculate and understand. Other than winning the lottery, in which the odds are pretty easy to calculate, we might be surprised how likely some events are. Dawkins in the book I mention goes through a pretty interesting argument concerning an antique watch that his wife buys for her mother. Without noticing when she gave the gift, her mother opened it and there were initials carved in the back that were the exact same as her mothers. So Dawkins does some actually calculations by going through the phone book and looking at how common certain letters are to start first names and surnames, and for a populations the size of the UK he found that the event could have happened to 2000 or so people. So it’s rare given the population of the UK, but not so astronomical as we often make it out to be. So I don’t want to give the impression that improbable events aren’t actually improbable, only that it’s easy to misunderstand the rareness of event, and that even for rare events, they are going to happen, and in a large population often. Another good example is that looking at the total number of homicides each year, there is approximately 50 homicides a day, which puts your odds at being murdered each day at 1 and 200 million. That is a pretty rare event. But if you hear about 50 murders a day because you get news from all over the states and those stories add up to 15,000 murders a year, you start to get a skewed perspective of how often a murder happens. So one might think murders happen frequently. And of course the 1 and 200 million odds is just a straight calculation out of the total homicides, divided by the population of the U.S. divided by the number of days in a year (I ballparked it by the way lol). But of course your odds are much less or greater if you live in rural areas, suburbs, or inner city. There are probably other geographic differences also. Furthermore your odds go up or down even more if you piss off the wrong person, have a gun in your house, cheat on your spouse etc.

Okay, I think I see what you’re saying. Thank you for the clarification. Well then in that case I wholeheartedly agree with you. Especially the part about how we tend to overestimate probability.