Originally Posted by void *
You can't actually make the statement that it is "quite a statistical feat" without being able to determine how many trials actually occurred.
If you have a probability of an event occurring of 0.00000001, if there is one shot at it the probability of one success is, naturally, 0.00000001
If there are 1000000000 trials, the cumulative probability that there is more than one success exceeds 0.997. That's 99.7%. The 0.3% left over is the probability that it happened either 0 or 1 times. The probability it happens /at least once/ is so close to 1 that the calculator I used just states 1. It's practically a certainty (although this hypothetical event could still not happen).
It doesn't matter how low the probability of an event is for a single trial - a sufficient number of places in which the event has a chance of occurring will raise the probability of that event, sometimes to near-certainty.
Please consider that before you decide that something is "quite a statistical feat", and ask yourself if you (or anyone) currently even knows in how many places in this gigantic universe we exist in conditions were sufficient to be considered a "trial". We know there's at least one. What we do not know is how many trials are hidden in that 'at least'.
A good way to explain this to people...
Go find the largest parking lot you can. Pick a car at random, and look at the vin#. What are the odds that you were going to find a car with that vin? Effectively zero.