Mathematician John Allen Paulos offers these worthy thoughts on the subject of creationist arguments based on probability theory:
But there’s another contributing factor to this opposition to evolution that I’d like to discuss here. It is the concerted attempt by creationists to dress up in the garb of mathematics fundamentalist claims about human origins and to focus criticism on what they take to be the minuscule probability of evolutionary development. (Even the conservative television pundit and ace biologist Ann Coulter has lent her perspicacity to this mathematical endeavor in her recent book.)
Sadly, I know from personal experience that this is true. I attended an ID conference in Kansas City a few years ago. One of the speakers was from the right-wing Heritage Foundation, and he spoke about probability theory a la William Dembski. At one point he whipped out some numbers, multiplied them all together, and then claimed that the tiny number that emrged represented the probability of some complex structure evolving.
During the ensuing Q&A one young man, with a look on his face that can only be described as comically serious, asked something like, “When atheistic scientists are confronted with probabilities that small,” dramatic pause, “how can they do anything except stare helplessly at it?” Heritage guy agreed that this was very puzzling.
So I raised my hand and informed the previous questioner that scientists respond by challenging the assumptions that went into the calculation, which in this case were universally false. I also mentioned several other variables that would have to be taken into consideration to have any hope of performing a meaningful calculation. The previous questioner gave me a look of such malevolence I decided not to pursue the issue any further. Heritage guy dodged the question and then went on to someone else.
This was hardly the only time that happened. When I attended the major young-Earth conference in Lynchburg last year, one of the best received talks was an attempt to use information theory to refute evolution. As I pointed out in my report on the conference, he received a standing ovation despite the fact that his arguments were utterly incoherent. The fact is that mathematics is unique in its ability to bamboozle lay audiences, which makes it well-suited to creationist ends.
Anyway, Paulos makes the central point:
This line of argument, however, is deeply flawed.
Leaving aside the issue of independent events, which is too extensive to discuss here, I note that there are always a fantastically huge number of evolutionary paths that might be taken by an organism (or a process) over time. I also note that there is only one that actually will be taken.
So if, after the fact, we observe the particular evolutionary path actually taken and then calculate the a priori probability of its being taken, we will get the minuscule probability that creationists mistakenly attach to the process as a whole.
Misunderstanding this tiny probability, they reject outright the evolutionary process.