For it to happen, for as many generations are their have been human generations, and for as many generations as there has been life, every single one of your ancestors needed to meet exactly the right mate at exactly the right time and to produce one of your ancestors with exactly the right combination of genes. In each generation the right sperm needed to fertilise the right ovum.
And if any one of these had been different, you would not exist.
So how to calculate the probability of you existing? Don't bother to do the math; the result is so small that it would have more zeros after the decimal point than there are elementary particles in the universe.
And yet you exist.
Isn't this evidence of a controlling force; some intelligence running things? How can something so hugely improbable happen at all? Well no. That view only makes any sense if you assume the purpose of everything was to produce you.
Let's do a little experiment.
Take a standard pack of cards, shuffle it well, and deal four hands of 13 cards. Now calculate the probability of all four hands being dealt in that order with exactly those sequences of cards.
Well, okay, I'll tell you. It is 1 in 53,644,737,765,488,792,839,237,440,000
Now take another pack, shuffle it and deal again. Do this ten times in all so you have forty hands
What is the probability of dealing those forty hands in exactly that order?
It's... well... vanishingly small, actually. Again, more zeros after the decimal than there are elementary particles in the universe.
You might feel justified in thinking this can't be mere chance. How can you have dealt exactly those forty hands when the probability against you doing it are so astronomical? Surely it was impossible for all practical purposes, wasn't it? Such a vastly unlikely outcome can't be due to mere chance, you might think. Surely such a vastly unlikely event happening could only be caused by some super power; some vastly intelligent; vastly powerful being with total control of everything - couldn't it?
And yet you have just achieved this seemingly impossible task with hardly any effort at all.
And that's where the mistake is.
Actually, the chances of you dealing forty hands is almost certainty, failing some event stopping you in mid deal, so to speak. The only thing that isn't certain is just what these hands will contain. But they WILL contain cards.
The chances of a human being born are almost certainty (once humans had evolved) and failing some catastrophe like a comet strike, the sun exploding or climate change causing extinction. The only thing that wasn't certain was exactly who those humans were going to be; exactly what genes they contain.
And if it hadn't been you, you wouldn't be reading this now.
Was there anything in that process which designed those forty hands and made them inevitable? Is there any design to be explained? Not unless you were trying to deal a pre-determined set of forty hands. If you WERE, then there is some explaining to do. It's so unlikely that a trick would be far more likely...
Still not convinced?
Okay, try this thought experiment:
Imagine you could write down the name of every person who ever lived, say 100 people to a page, and 100 pages to a book (10,000 people to a book). Lets assume the number of people who have ever lived is 100 billion. This would give you 10 million books.
Now, imagine you could arrange these books on two shelves on opposite walls of a vast library.
Now flip a coin. If heads, eliminate the right hand wall; if tails, the left.
Now flip a coin again. If heads eliminate the right hand half of the remaining shelf; if tails the left.
Continue this process until you have one book left.
Now flip a coin to decide which half of the book to eliminate. Continue this until you have just one page left.
Flip a coin to eliminate to top half or bottom half of the page.
Continue this until you have just one name left.
Is there anything special about that person? If so, you could repeat the process and arrive at the same person, couldn't you? And yet the probability of doing so is 1 in 100 billion.
Yet this person needed every one of some 37 consecutive coin flips to be correct in order to be selected. Probably as unlikely as winning the National Lottery every week for a year.
But the probability of SOMEONE being selected was certainty. No explanation other than chance is required, UNLESS the intention was to select that one individual. Only then we would need to explain it in some way other than random chance.
Was there anything in that process which designed that particular result? Did you require any super-powers to achieve it?
Nope. It was all pure chance and it produced an astronomically unlikely result. And yet A result was certain. It is not the fact of a result we need to explain. An explanation is only required to explain a particular pre-determined result.
Yes, it was astronomically improbable that you would be here, now.
But there was no designed intent to produce you. No one intentionally produced exactly you with exactly your genes and exactly your life.
So there is no explanation needed beyond pure chance because there is actually nothing to explain.
And it's this huge unlikelihood of you having this chance to experience life which makes you special; not the notion that there was some pre-determined intent to produce you. Had that been so, there would be no wonder in your existence. You would be nothing more than a conjuring trick; easily understood by the simple-minded but nothing more to be said or discovered.
As it is, your existence is truly wonderful.