Briefly, the argument from improbability says that such-and-such an event is so enormously unlikely that it couldn't just happen by chance, so there must have been a creator, or, in the words of Creationism's under-cover wing, 'Intelligent Design', an intelligent designer (i.e the god they are trying hard not to mention). Events such as the origin of life, the origin of the first cell, a human body, the human brain, a tree, etc, etc, etc, will be cited ad nauseum. This argument is, of course, used for any god by any religion which has a creator god. The actual god doesn't matter; you're just expected to assume it's their favourite one.
The appeal of this argument seems to depend on both ignorance and arrogance for its success. It seems to give its proponents the spurious satisfaction of having an argument which simultaneously circumvents and dismisses the need to bother with all that learning and yet enables them to present themselves as knowing more and having greater insight and understanding than those who do so bother. And yet, as Richard Dawkins pointed out in "The God Delusion", properly deployed, the argument from improbability comes close to proving that God does not exist.
But it is, of course, invariably a straw man argument combined with a false dichotomy. Biology does not make any claim that cells or bodies, brains or trees, or even the first replicators spontaneously self-assembled by chance. So the choice is not between random and hugely unlikely chance or design/intent. It is between random chance, intelligent designer or a process of natural selection over a very long time. For some reason, religious apologists and Creationists conveniently forget to include Natural Selection either because they don't understand it or don't want you to.
I'll let Richard Dawkins, quoted from "The God Delusion" in Christopher Hitchin's book, "The Portable Atheist: Essential Readings For The Non-Believer", explain it:
The Ultimate Boeing 747
The argument from improbability is the big one. In the traditional guise of the argument from design, it is easily today’s most popular argument offered in favor of the existence of God and it is seen, by an amazingly large number of theists, as completely and utterly convincing. It is indeed a very strong and, I suspect, unanswerable argument — but in precisely the opposite direction from the theist’s intention. The argument from improbability, properly deployed, comes close to proving that God does not exist. My name for the statistical demonstration that God almost certainly does not exist is the Ultimate Boeing 747 gambit.
The name comes from Fred Hoyle’s amusing image of the Boeing 747 and the scrapyard. I am not sure whether Hoyle ever wrote it down himself, but it was attributed to him by his close colleague Chandra Wickramasinghe and is presumably authentic. Hoyle said that the probability of life originating on Earth is no greater than the chance that a hurricane, sweeping through a scrapyard, would have the luck to assemble a Boeing 747. Others have borrowed the metaphor to refer to the later evolution of complex living bodies, where it has a spurious plausibility. The odds against assembling a fully functioning horse, beetle, or ostrich by randomly shuffling its parts are up there in 747 territory. This, in a nutshell, is the creationist’s favourite argument—an argument that could be made only by somebody who doesn't understand the first thing about natural selection: somebody who thinks natural selection is a theory of chance whereas—in the relevant sense of chance—it is the opposite.
The creationist misappropriation of the argument from improbability always takes the same general form, and it doesn't make any difference if the creationist chooses to masquerade in the politically expedient fancy dress of “intelligent design” (ID). Some observed phenomenon—often a living creature or one of its more complex organs, but it could be anything from a molecule up to the universe itself—is correctly extolled as statistically improbable. Sometimes the language of information theory is used: the Darwinian is challenged to explain the source of all the information in living matter, in the technical sense of information content as a measure of improbability or “surprise value.” Or the argument may invoke the economist’s hackneyed motto: there’s no such thing as a free lunch — and Darwinism is accused of trying to get something for nothing. In fact, as I shall show in this chapter, Darwinian natural selection is the only known solution to the otherwise unanswerable riddle of where the information comes from. It turns out to be the God Hypothesis that tries to get something for nothing. God tries to have his free lunch and be it too. However statistically improbable the entity you seek to explain by invoking a designer, the designer himself has got to be at least as improbable. God is the Ultimate Boeing 747.
The argument for improbability states that complex things could not have come about by chance. But many people define “come about by chance” as “a synonym for come about in the absence of deliberate design.” Not surprisingly, therefore, they think improbability is evidence of design. Darwinian natural selection shows how wrong this is with respect to biological improbability. And although Darwinism may not be directly relevant to the inanimate world — cosmology, for example — it raises our consciousness in areas outside its original territory of biology.
A deep understanding of Darwinism teaches us to be wary of the easy assumption that design is the only alternative to chance, and teaches us to seek out graded ramps of slowly increasing complexity. Before Darwin, philosophers such as Hume understood that the improbability of life did not mean it had to be designed, but they couldn’t imagine the alternative. After Darwin, we all should feel, deep in our bones, suspicious of the very idea of design. The illusion of design is a trap that has caught us before, and Darwin should have immunized us by raising our consciousness. Would that he had succeeded with all of us.
Hitchens, Christopher (2007-12-10).
The Portable Atheist: Essential Readings For The Non-Believer (pp. 288-289). Perseus Books Group. Kindle Edition.
- We can agree with Creationists that random chance is far too unlikely to be the explanation. No argument there; it's just too daft for words. Invoking random chance as the explanation for anything of very much complexity is probably the daftest argument you can come up with. Let's call this 'The Laughably Absurd Hypothesis'.
- We know that there is a perfectly well described and understood process called Natural Selection which we can observe, and which is probably the most tested, robust and evidentially supported theory in the whole of science and which we know is quite capable of producing huge complexity over time. Let's call this 'The Very Probable Hypothesis'.
- We have a vague, very incomplete and poorly described Intelligent Designer Hypothesis. The problem with this is that it collapses immediately under the weight of the very problem it purports to solve. It requires us to abandon the idea that hugely complex things are very unlikely to spontaneously self-assemble - the thing we were trying to explain - and adopt instead the notion that 'The Laughably Absurd Hypothesis' is not only not too daft for words but that somehow it's now the best explanation available and a vastly complex intelligent designer, complete with all the information necessary to create the universe and everything in it, spontaneously self-assembled and did so before there was anything out of which it could be assembled - which is of course logically absurd on so many levels - and Creationists themselves are forever assuring us that you can't get something from nothing. Let's call this 'The Logically Impossible Hypothesis'.
Now, the task for those Creationists who have managed to get this far before closing the page in embarrassment is this:
Explain please, why your 'Logically Impossible Hypothesis' should be taken seriously by anyone with an IQ higher than that of a thick plank, and in what way it is superior to either of the other two.
If you can't, which of the other two competing hypotheses do you think is most likely to be the true description of how complex things arise: The Laughably Absurd one or The Very Probable one?
Take your time.