To the nearest order of magnitude, there have existed, including us, about 100 billion human beings. This proves what was always, until our day, quite obvious: that people are good at breeding. (Or were, before discovering contraception and abortion, of course.)

That’s a lot of people in a relatively short period of time, geologically speaking. Humans have only existed some few hundred thousand years.

According to Harvard Law blogger Ali Binazir, author of Awaken Your Genius, you, dear reader, only have a “1 in 10^{2,685,000}” chance of existing. Pretty small, no?

But since there’s been so many of us, each one of us being next to impossible, something has gone wrong in the calculations or our thinking.

Nothing better illustrates the truth that all probability is conditional than Binazir’s calculation. It’s sort of a Drake equation for individual human existence. The Drake equation is a probability-like calculation which gives the chances of other life forms like us, i.e. rational, existing on other planets. It is notorious in its liquidity: it won’t stay solid. Binzair’s calculations suffer from the same flaws: he’s unable to keep straight which side of the equation he’s on.

Given you’re reading this post, the probability you exist is 1, i.e. it is certain. That’s because there must be a you to read. But Binazir tells us that the probability you exist is a number nearly equivalent to 0, the other end of the probability spectrum. Both probabilities can be right, since all probabilities depend on the premises used. Depends on the meaning of “to exist”, also. Does it mean “being made” or “alive and functioning now”?

Alive and functioning now is easy: you exist certainly. But how did you get made? Well, mom met dad and they did what came naturally. Out came you. You, logic insists, could not be other than you. This is necessary to emphasize.

The probability *your* parents had *any* kids is also 1, because you are one of them. But the probability that two mated humans reproduce is different. That probability doesn’t exist because no premises have been specified. One possible premise: both over 80 years old? Another: one is sterile, by natural or artificial means. Another: one is forever on the road. And on and on.

Now each time the mates attempt to reproduce, either a baby is produced or it isn’t, a tautology. In either case, something caused the baby to be made or to stop it from being made. We (typically) won’t be in the position of knowing these exact causes, so we say the creation or lack of it is “random”, which is just another label of our ignorance of the causes. But if we assume these causes are “regular”, and are careful to specify the kind of mates to which they apply (say, 20-30 year-olds, of this and such background, etc.), then we can use probability to express our incomplete knowledge and make reasonable predictions over groups of mates.

In any case, we are not asking what is the probability your parents had kids, because they obviously did. We asking the probability of you yourself coming into being. Assuming each of your mom’s and dad’s gametes were unique (are male gametes like snowflakes? has anybody checked? I ask in ignorance), then each mating could make a different baby. But each mating will have a list of causes which either make or stop the baby. So again we’re not talking about what causes the individual gametes to meet.

What premises to use? Any individual attempt? Thus the number of male gametes and a fixed female gamete. In ignorance of the causes, and assuming conception, there are n male gametes and one female, thus the probability is 1/n that this male gamete meets this fixed female one. Is that newly created baby you or somebody else? Assuming no conception, then no you and no anybody either. What is the probability of no conception? Well, what premises do we assume?

You can see this is getting nowhere slow.

The problem is in the question. What is the probability *you* exist? This is not what is the probability somebody else exists, or the probability somebody in your place exists. It isn’t even the probability some other human exists—which is one by the plain meaning of the question. Why? Because people exist.

You exist, too. Therefore it must be the probability you exist is 1. That you might not have existed is a counterfactual question, which is perfectly comprehensible as long as we supply the premises under which you would not have existed. Say, you imagine your dad got called away on a business trip during the time in which your parents conceived you. Or that your dad never met your mom. Then, given those premises, the probability would *not* have existed is also 1, because there would have been no causal way of you coming into existence.

Face it. Probability is never as easy as you hope it is.

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*Thanks to The Carolina Cowbody for suggesting this topic.*