This is Goblinono's response to an article "A Mathematical twist on the Fermi Paradox" from Discovery News at this address - http://news.discovery.com/space/a-mathematical-twist-on-the-fermi-paradox.html#mkcpgn=rssnws1
"Considering that our existence on this planet is probably the result of a random event that was a legacy of all the evolving forces of the universe, mathematically our existance should not exist in the realm of probability but in the realm of improbability. If we consider the size of the universe, its age and the direction of light travel (that depends of course on whether the universe is expanding or contracting!) and then factor in all the information about the universe that we are not yet privy to because of our young age and limited technology we may find that we are in fact THE ONLY incidence of a chance occurence in this great cosmological melting pot. The odds of this happening are incedibly high - and it seems to me that if the odds are so against this chance event, then we probably are THE ONLY civilization to have occured as a random event.
The essence of probability theory was developed in the 1600's from a partnership between a gambler (de Mere) and 2 mathematicians (Pascal and de Fermat) and it was postulated that if an event had a lesser chance than one in a hundred, then it probably would not happen.
There is also a mathematical problem presented by the 'inspection paradox' - the probability distribution of a quantity that has already started its life is shifted, leading to a larger average than would otherwise be expected. For example : when you wait for a bus, the distribution of bus interarrival times has already started.
In other words - if you were an apple in a bunch of apples inside a spinning bag hung from the ceiling it would be hard to be objective about your position unless you removed yourself from the bag - and then you would no longer be included in the sample you were studying - so the odds have changed yet again!"