The figures being batted around here are correct for the probability of this particular macro-event's occurring here and now. But there is a statistical fallacy involved in drawing from this the conclusions that are being drawn.
This well-known fallacy, but I don't know if it has a name, let me baptise it "the cash-register fallacy", is as follows: you have just dumped a week's worth of groceries on the cashier, they ring it all up, it totals to $77.11 and they say, "wow, look at that. What are the odds of that happening?" Well, the odds of this particular striking lucky number's happening were 1/10,000. But there are so many other striking numbers that would have produced the same impression, that when you add them all up.... it is not so unusual. In fact I have had to listen to cashiers say the same thing to me five times now, and have stopped buying groceries.
The relevant probability that needs to be estimated is the probability for "a striking macroscopic event" to occur, and to estimate this, we need to count how many
(independent) types of such events there are, just as above someone once estimated how many striking five digit numbers there were. No physicist has ever performed this estimate. No one has any idea how to do it, and I suspect it could affect the conclusion.
Something similar to this fallacy has been present in the history of debates about whether random Natural Selection can indeed be the real motor of evolution. Around 1900, opponents of Darwin's theory of random Natural Selection used the same general line of reasoning as some of the professional physicists contributing to this site. Sir Ronald Fisher exposed the fallacy involved. Currently, some scientists (they might be associated with the so-called "Intelligent Design" agenda, but I cannot tell for sure) are offering a million dollar prize for anyone who can show that the probabilities for random mutation acting with Natural Selection's producing six detailed biochemical processes which are key to life as we know it, over the time-span in which the Universe has been in existence, acting at a certain rate of operations per second, are at all plausible.
They are falling into the same statistical fallacy as is present in the other post here. The relevant probability that needs to be estimated is not the probability that these six particular mechanisms could have been produced by chance, but the probability that any of God only knows how many possible alternatives that would work, even though they did not in fact happen, and produce "life", could have arisen through chance.
Unless and until someone can estimate how many different independent alternatives there are, no assertion can be made about the probability of life's having arisen through chance alone. And similarly here, none of the posters have the right to make an assertion about the probability, during the total career of the Universe so far, of a macroscopic violation of entropy's occurrence. Here, though, I think it might be feasible to estimate how many different independent types of violations should be counted.
Falling into this fallacy is related to the failure to undertand the difference between a micro-state and a macro-state, a misunderstanding endemic to students of Stat Mech and Thermo. All micro-states have the same probability as each other: nearly zero! The only physically relevant probabilities are the probabilities of the different macro-states. Here, we have to figure out which is the relevant macro-state. The wrong choice will lead to a calculation lacking any significance. The wrong choice has been made in these posts, and by the anti-Darwinian people behind the offer of the prize, and the results of the calculations are physically meaningless.
Up to here is what interested me the most. But there is one more point to be made: the Universe is not in fact in a state of equilibrium: this is obvious to the naked eye. It seems as though the mixing process has not yet gone on long enough. So none of the laws of thermodynamics even apply to the Universe as a whole. So the extrapolation from the probability here and now to the probability over the life-time of the Universe is also invalid.