People Don't Understand Probability

For my first substantive post here I'm going to take a look at an issue that's bugged me for some time. Reading a recent article written by Ervin Laszlo that once again demonstrated the problem is actually what finally pushed me to go ahead and start blogging.

The argument he presents is one a lot of people throw around without really understanding what they're saying. It can be basically summed up as "This thing happened... it was amazingly unlikely this thing happened by chance... therefore something must have caused/created/designed it." In order to illustrate why that article is completely wrong I usually find it's easier to deal with a different example of highly improbable outcomes occurring.

The odds of winning the Powerball lottery purchasing a single ticket are roughly 1 in 195 million. Let's say last week Joe Lucky bought one ticket and won the jackpot. The odds of him doing this by chance were, as stated, 195 million to 1. That's ridiculously unlikely. Do we therefore conclude the lottery was somehow designed to make him win since it was so unlikely that he would win by chance?

No, we don't. Most people understand that we don't. What most people do not fully understand is the reason we don't.

An event being unlikely... no matter how astronomically unlikely it is, is simply not evidence of "rigging" of a process. Because the fact of the matter is it was unlikely for ANY specific person to win the lottery. But the odds that someone would win were pretty decent considering how many people were snapping up tickets. No... Joe winning is not suspicious.


Let's say that the night before the drawing I make an announcement. "Joe Lucky, who bought a ticket in the middle of nowhere Idaho yesterday, is going to win tomorrow's powerball drawing". And then he does. Now we're getting into interesting territory and need to be looking for foul play.

"But Grant", you might say, "what's the difference between you guessing who would win and Joe guessing what the winning numbers would be"? All the difference in the world actually. See, on one hand we have millions of people wildly picking numbers out of a list and just hoping that they end up matching the lottery draw, and one of them getting it right. On the other we have one guy who announces he knows exactly what result the lottery draw is going to produce and getting it right in one try.

To try and make it more clear why that makes all the difference, let's switch metaphors for a moment. Now we're in an archery contest.

Somewhere, on a very large blank wall, you have marked a target in invisible ink. You then lined up a million archers to all shoot arrows at the wall. Odds are pretty decent that one of them is going to hit it, and we wouldn't think it suspicious if one of them did.

We would think it suspicious if I was able to tell you WHICH of them would hit it before any of them took their shot however. The evidence that something isn't right is that someone was able to clearly call the outcome of the process ahead of time when that shouldn't have been possible if the process wasn't rigged. Going back to the lottery, same principle. It's not the improbability of the event occurring (Joe winning) that is evidence of rigging. It's that someone was clearly able to call the outcome ahead of time when they should not have been able to do that in an un-rigged situation.

Now, I would hope that it becomes clear why the article I linked at the beginning of this post is wrong. But to walk through it, this is the argument it made:

1. Evolution of life on earth was extremely unlikely.
2. It only happened because conditions in the universe existed to enable it which were also mind bogglingly unlikely
3. Therefore this is evidence the universe was designed ("rigged") to produce this very unlikely outcome.
4. Therefore there is some supreme entity that did the designing.

But what do we need for evidence of rigging? Someone had to call the outcome in advance. Which means the only way you can make this argument is to begin by assuming that call was made. Which means you've assumed your conclusion before you started and are engaged in an act of circular reasoning. You might as well have just said "assuming evolution was designed, it would be really unlikely to go exactly according to plan by chance... therefore it must have been designed!" Sorry, but you have to prove there was a plan first before trying to claim evolution improbably matched it.

Yes, the way the universe turned out was unlikely. If it had turned out any other way however that would have been equally unlikely. And that wouldn't have been any more evidence something designed it to happen THAT way then the universe turning out the way it has is evidence something designed it to turn out THIS way. And anyone who argues otherwise should also be telling us every lottery ever conducted was clearly rigged since it was so amazingly unlikely that whoever won it would win it by random chance.

People who make this "the universe was fine tuned" argument don't understand probability.


  1. I have a feeling that the probability of life occurring out of an eye of water should be seen as 1^N, where N is very large, and the probability of not occurring is 1^N-1, thus very, very large.

    And, after all, why is there a lottery for this in the first place? Which is the probability for the dice to be thrown or not? Is it 1 because they have been thrown? But why and who's playing with us?

  2. Sorry for the delay approving that comment, I wasn't paying attention to the moderation messages.