## 2007-09-14 00:57

# The unfatomable improbability of my existence.

I am doing this as a public service for USA readers, because you are likely to be in contact with someone who believes evolution of life is incredibly unlikely. After all, many of your presidential candidates don't believe in evolution. Which would be sad if it wasn't because I expect some of them do but are afraid of losing the ignorant religious fanatic vote (which makes it just lame).

You will sometimes see someone say something like "that's unlikely!. The odds of A are 1 in 1000 and the odds of B are 1 in 500, so the odds of A **and** B are 1 in 500000!".

This argument is very, very, very wrong. But for those with an intuitive knowledge of probability it looks good, because they know that the odds of a coin flip coming heads is 1/2 and the odds of 2 consecutive heads is 1/2 * 1/2 = 1/4 and so on.

Now, let's construct me this way (warning: made up numbers ahead).

I am argentinian. There's roughly 35M argentinians out of 6000M humans. That's about 1 in 171.

I am male. That's about 1 in 2.

I am a bit over median height. That's also 1 in 2.

I have a beard. I am guessing 1 in 10.

I wear size 41 shoes. That's about 1 in 4.

I use glasses: I'd say 1 in 5.

I get dizzy riding buses: About 1 in 100.

I am married: 1 in 4.

I have a child: 1 in 2.

I have a son: 1 in 4.

He is 4 months old: 1 in 200

So, I have a 1 in 87 552 000 000 chance of existing. And I could make those odds much lower. After all, I was born in 1971, mi favourite colour is green and my name is Roberto.

There are two reasons why you should never trust this kind of number manipulation unless you really, *really* know what you are doing.

- You can't just multiply anything. These odds have to be about
*statistically independent variables*.

For example, I get 1 in 8 from having a child, and having a son.

Yes, maybe the odds of someone having a child are 1 in 2, and the odds of someone having a son is 1 in 4, but those are **correlated**. The odds of having a son *if you have a child* are about 1 in 2. The odds of having a child if you have a son are 100% :-)

If two variables are correlated you can **not** multiply their probabilities.

A much sillier example.Imagine there are ten countries, each with 1 tenth of the population.

The odds of being from A is 1/10.
But he is also **not** from B,C,D,E,F,G,H,I, **or** J! There's a 9/10 chance for each one of those facts!

So, the odds of being from A and not fromanywhere else is 1/10 times 9/10 ... that's almost 1 in 26!

And since the same reasoning applies to each country, it turns out there is almost a 60% chance the next baby will not be born in any one of the ten countries.

See how stupid that sounds? Of course when correlation is more subtle, it's harder to figure out, and you will not be able to do this while arguing.

- Add random unlikely data.

This is slightly trickier, because it may be what you really wanted to do. Yes, me being **exactly** the way I am is extremely unlikely. However, something more or less like me is not.

Yes, I am unlikely but that's trivial. However, if you are going to apply this kind of reasoning in other cases it gets silly quick. Here's an example:

Imagine a lottery with 6-digit numbers. Today, the winner is 123456. Yesterday it was 654321.

The odds of those numbers being the winners is 1 in 1 000 000 000 000. But it's obvious that if you make two draws, **some** two numbers will come up! And whatever they are, they will be just as unlikely!

That something **specific** is unlikely doesn't always matter, because the important thing is the chance of some **kind** of thing happening, not of **one specific** thing.

And when/if you have a kid,and he/she/it asks you why he should study math, show him his kind of thing and tell him why:

**Math makes it harder for people to lie to you.**