The classic argument from design is as follows: The universe is ordered. Unless there is a God, it is unlikely that the universe would be ordered. So, given the orderliness of the universe, God is likely to exist.
The argument has intuitive force. Designed things have designers. Order is a result of design so our observation of order leads naturally to the conclusion that the universe has been designed by a designer.
Here is a good criticism from inverted probability. Simply put, to invert probability is to take an argument such as the design argument and switch it around. So,
A. "given the existence of God, the universe is likely to be ordered"
is inverted to render:
B. "given the orderliness of the universe, it is likely that God exists"
A. is very plausible. If God designed the universe, he would do so in an orderly manner. However, some philosophers argue that the inversion in the case of the design argument does not give us what we want. In other words, A. does not give us B. To see this, Graham Priest asks us to can consider the probability of a person being in Australia, given the fact that he has seen a kangaroo in the wild. It seems, in this case, the probability of the person being in Australia would be quite high considering that Australia is the only country in which there are wild kangaroos. However, from this premise one cannot gauge the probability of that person seeing a kangaroo in the wild, given that he is in Australia. Even if one lives in Australia, seeing a kangaroo in the wild is quite rare.1
So, if the probability of an ordered universe is high, given that it was created by God, that doesn't mean we can infer that the probability of God existing is high, given an ordered universe.
Why not? Well it has to do with prior probabilities. If the prior probability of God existing is no more than the probability that God does not exist, then it fails to give B. So, is it? Well, it depends. If one is allowed to offer other arguments for the existence of God to increase the prior probability of his existence, then, yes, it might raise the probability high enough for B. But if one takes the argument from design alone, the prior probabilities don't count in the favor of the theist.
Consider the kangaroo argument. The prior probability for "given that the person has seen a wild kangaroo, it is likely that he is in Australia" is the fact that the only country in the world that has wild kangaroos is Australia. If you see a wild kangaroo you can be pretty sure you are in Australia. But what are the priors for the probability of God designing the universe? Well, if one does not believe in the necessary existence of God (and the design argument does not depend on God's necessary existence), then one might come up with a host of other explanations. David Hume suggested demons, many gods, and laws of nature. A contemporary critic might add evolutionary theory. The priors, in this case, don't help.
Priest claims that we need not posit alternative explanations to reduce the probability of God's existence. He claims that "there are many ways that the cosmos could have been. And, intuitively, relatively few possible cosmoses in which there is an orderer." He concludes that the prior probability of God's existence is actually lower than his non-existence.
One way to respond is to suggest that the probability of an ordered universe without God is low given the many ways in which the universe could have been none of which would be life-sustaining. The fine tuning–argument is kind of design argument. The fine-tuning argument makes the probability of there being an ordered universe that sustains life so low as to require an explanation. The fine-tuning argument increases the probability of the following: "given the ordering (and life-sustaining features) of the universe, the probability of there being no God is extremely low." The fine-tuning design argument's conclusion is "given the probability of a life-sustaining universe being the actual universe, it is likely that God exists." It is still open to the a-theist to claim that there are alternatives to gods that work - multiverses, aliens and alike. But the simplest explanation is that God created and ordered the universe.
I'm not so sure Priest's objection is as sticky as he would like. The point of the design argument, especially its fine-tuning version, is that the actual universe is life-sustainingly-ordered. The simplest explanation is that God chose this universe rather than a universe that is not life-sustaining. The prior probability claim is not that there is such a thing as a life-sustaining universe, but that this particular universe is life-sustaining. Consequently, I think Priest's criticism misses the mark.
1 Graham Priest, Logic (New York: Sterling Publishing Company, 2000), 118–119.