Many of you have probably at some point come across the creationist argument for probability which often uses calculations to make the case that the formation of the universe and life could not have arose by "chance." This argument differs slightly from the argument for intelligent design in that it not only examines the alleged complexity, design, and order of structures (for example examining the complexity/design of a molecule), but the probability that each component of the universe needed to sustain life could have developed independently and function seamlessly. This argument is commonly used to try to disprove abiogenesis and strives to demonstrate that earths position in the universe is too perfect to have gotten there by chance (Goldilocks argument). The calculations made to support these arguments result in staggeringly huge numbers like 3.34 x 10^450 and are usually followed with Borel's law.
Without even thinking too hard about it, I see a few things wrong with this argument
1) It assumes that that the development of the universe is random, when in reality it is driven by the laws of nature
2) The universe is practically infinitely vast. For the one planet that did develop within a life sustaining solar system, there are countless others that did not.
3) It only looks at the way life DID develop ex post facto instead of all the ways it COULD HAVE developed with only slightly different conditions.