The odds of that rock being in that exact place on this planet given a random big bang are very very close to zero, but to talk about that is simply crap.  SOME universe exists, and we’re standing in this one, so it’s the only one we can talk about.  In any other universe, we wouldn’t be here asking the question.

I think the odds that all of my ancestors were able to reproduce is pretty great… that’s why they are my ancestors. The odds are certainly greater than the possibility that one of my ancestors spontaneously generated into existence.

It’s certainly true to say that the odds of a single-celled organism’s genetic material surviving for 4 billion years to become a multi-celled organism is great. But it doesn’t work in reverse. That’s like saying the odds that my wooden chair came from a tree is equal to the odds that any one tree will become my wooden chair.

Now let’s think about you.  You have a height, which is finite, of course.  Let’s call it Y feet.  Now, what is the probability that a random person off the street would have height Y?  zero.

Probability of boy meeting girl: 1 in 20,000.
So far, so unlikely.
Now let’s say the chances of them actually talking to one another is one in 10.

…all I can say is, he obviously never met my mother. :-)

The chances of her meeting a man she found attractive but then NOT talking to him were… well, maybe one in eleventy bazillion or so.

I believe that barring mutation, all X-carrying sperm are genetically identical and the same for all Y-carrying sperm.

But your believing it doesn’t make it true. :-)

Go look up Meiosis.    We’ll wait.

So I’d guesstimate that, for my daughter, that first 1:40,000,000 probability would improve to about 1:50 or better.

The non-uniqueness of sex cells issue, discussed below, should pretty much negate that whole term, though post-conception variables would open up a whole ‘nother can of worms.

Second, this highlights the difference between permutations and combinations.  A permutation is any specific set of event outcomes.  Flipping a coin four times and getting H, T, H, T is one permutation, getting H, H, T, T is another.  A set of permutations with a specific number of each event outcomes is a combination.  The permutations both listed are both examples of the combination two heads and two tails.

Let’s say I flip a coin 500 times.  Getting any one predetermined sequence of heads and tails is phenomenally unlikely, so there is a low probability for that permutation.  Getting  250 heads and 250 tails, in any sequence, is much more likely – the probability of this combination is the sum of the probability of each combination where there are 250 heads and 250 tails.

The infographic  gives the probability of the permutation of the event outcome known as you.  The particular gametes that met (and all the necessary prior gametes meeting) and expressing themselves in a particular way is highly unlikely.  You are a permutation.  The probability of the combination of a person though – very likely.  Even the probability of the combination of a class of people like you is fairly likely, i.e. that you in particular might be unlikely, but the probability in this set of events of producing a tall man with brown hair who likes computers and Megadeth is much more likely.

Who was it that said “Remember, you’re unique – just like everyone else”?