J. P. Moreland sketches out three probabilistic arguments from design. They are all based on three different conceptions of probability; possibility, frequency, and evidential.
Possibility (the classical way of viewing probability; if any event can occur in y amount of different possible ways the probability of x is x/y. For example if one were to flip a coin or throw it at your dog the probability of it landing on heads is 1/2): Moreland points to two examples for the theist to deploy this concept into an argument: the values of cosmic singularities or in the development of life. When talking about cosmic singularities and the like we mean that certain values seem to be necessary for life or for the big bang to occur the way it did. Now if these values (like the expansion rate of the big bang) could have been different there is a possibility probability (we could say for example that the chances of any value x obtaining are x/y). But can we set up a possibility probability for cosmological constants and singularities? No we can't. This is because we do not know the value any constant can take; in the x/y probability we do not know the y. Because of this when we say that the value of the expansion rate of the big bang could have been otherwise we are setting up a probability as follows: x/? and this is obviously not a very promising probability for anything. For all we know the possibility’s that the x could have obtained could be 1/1 or 1/infinite. However when we are talking about the chances of life developing this could be a much more promising argument, though unfortunately he does not write to much about this.
Frequency (a statistical view, to say that x is probable is to say that x occurred y amount of times and since y is a high number it would be reasonable to assume that x will occur again. For example if I flip a coin 65 times and it lands heads each time it would be reasonable to assume that it will land heads again on the 66th time): Moreland notes that this view is not very useful for the design argument however it may be able to strengthen the possibility view. For example he mentions experiments which display random results of the formations of protein. This would lead one to assume that the formation of protein occurred out of chance.
Evidential (this view asks to what extent does the evidence lead one to think that the chances of x occurring are reasonable or not so?): One could use this view to argue for God's existence based on the fact that y is more probable given God's existence then given atheism. This seems rather speculative but there certainly could be evidential arguments made for both atheism and theism. For example one could say life is more probable given theism or on the flipside evolution is more probable given atheism. Again it seems rather dubious how one could figure out how any event would be more probable given atheism or theism, but it would be interesting if one were to make a chart or something of all the things that may or may not be reasonable to expect given atheism or theism and how these things provide evidence for either position.
Moreland, J P. Scaling the Secular City. Grand Rapids,MO: Baker Books, 1987. N. pag. Print.