Chapters 14 and 15 of The Creator and the Cosmos are probability arguments based on the supposed improbability of human life occurring in our universe. Although both chapters argue that some set of facts is incredibly improbable, and this improbability requires divine intervention in order for human life to occur. The first is Fine-Tuning Argument and the second depends on the improbability of all the contingent features Ross claims are necessary for human life. I evaluate these two chapters together, even though they are distinct and involve distinct errors, because taken together they paint a picture of an absurdly impotent God.
The fine-tuning argument is that God has to "tune" the constants and laws of nature of the universe in order for life (or life as we know it) to be possible. If these constants were slightly different, it would not be possible for life (as we know it) to exist. It is then assumed that it is highly improbable that the constants have exactly these values. Hence, Ross concludes, the probability of life occurring is so low that we have to conclude that some being deliberately set up the conditions to allow for it.
The second argument is that it is incredibly unlikely that exactly the contingent conditions, say a planet in the right temperature zone for liquid water etc., for human life would occur in our universe. So we should conclude that God must have set up our planet specifically for our life.
The absurdity in making both these arguments is that they collectively entail a God who is so incompetent or powerless that he/she/it cannot create a universe whose basic laws and constants are such that life would become likely. In other words, Ross thinks that God set up a universe so that it would allow for life, yet God did such a crappy job of creating this universe that it does not in fact allow for life but requires God to intervene and create a world for humans to occupy. Perhaps it's just unbelievably hard for God to create a universe that allows for life to exist and also allows life to arise naturally. But such a response cannot be correct if we think God is an omniscient and omnipotent being. Such a God could create conditions that would allow life to arise naturally. And if God were going to create miraculously a world for human habitation, then he would have no need of careful fine-tuning.
These two arguments are individually unsound in any case. The problem with the fine-tuning argument is that there is no way to establish the probability that the constants and laws of nature might have been different. One could reasonably argue, to take a favored example, that, if you survived a firing squad in which dozens of marksmen all missed, then there must be a conspiracy not to kill you. This argument works because the probability that each individual marksman miss is known (and is very low), and so the conjunction of them all missing can be calculated to be extraordinarily low. Since the odds that they all miss by chance is vanishingly small (let's suppose), then we can conclude that there must be a deliberate agreement not to shoot you. However, in the case of the constants and laws of nature, we have no idea what the probability is that the constants differ from their actual values. Without that probability, there is no way to calculate the improbability that life would exist. So, following our other example, we cannot estimate the probability that there is a conspiracy not to shoot you unless you have some idea how accurate the marksmen are.
For the most part these arguments rely on the mere logical possibility that the values differ, but logical possibility tells us nothing about probability. It's logically possible that I turn into a chicken in the next second (this example I get from Abe Brummett), but that does not mean I should worry about it. The probability that I turn into a chicken is vanishingly small--or zero given the laws of nature. So, one cannot rely on establishing the logical possibility that these values differ in order to prove the improbability of them all lining up perfectly for life as we know it to be possible.
The second argument differs from the fine-tuning argument because it may be possible to give some ballpark estimate of at least some of the characteristics of the earth that may be necessary for life. Any such estimate would be highly unreliable, but at least there is some possibility of making such an estimate. Since the universe is incredibly large, with billions of stars in billions of galaxies, it's quite possible that our earth, of the billions possible, could meet those requirements. The extreme improbability of an event does not mean that it is impossible. Any particular person winning the lottery is very unlikely, but it is quite probable that someone will win. The difficulties are in estimating the number of factors that are, independent of each other, necessary for life (as opposed to life as we know it) and making an accurate assessment of these probabilities. As I said, it is not necessarily impossible to do this, but we should not conclude too quickly that our existence is impossible or likely.
Ross provides estimates of the probability of various factors, but he never explains how he arrives at these probabilities, so there is no way of evaluating his estimates.
Finally, we cannot make estimates only on the probability of life like ours is possible since the exact features of our lives are not relevant to the question of whether life in general is possible. Are we to estimate the probability that life would evolve bipedalism? That would be unlikely, one would suppose, but we cannot know that God would care about bipedalism (unless God is bipedal and wanted to create us in his/her/its own image!). So, Ross's claim that there is a .001 probability of having the right surface gravity (for example) is almost certainly too low a probability since we do not need gravity to be earthlike in order for life to develop. That gravity may not even need to be great enough to maintain an atmosphere since life might develop in liquid that would not escape even with the gravity of, say, a moon. I am not expert enough to substitute my own probabilities for Ross's, but it's unlikely that his low probability estimates are accurate.
I think that Ross is interested not just in the probability of life but the probability of intelligent life, and that is certainly much less likely. So, the probability of intelligent life must be much lower than the probability of life. However, the first problem remains. We have a great deal of uncertainty about exactly what is necessary for intelligent life and how probable those factors are.
But, perhaps more importantly, we need a better reason to think that God would want intelligent life to exist. These probability estimates only make sense if we think God wants some specific, improbable outcome. But why does intelligence matter to God? Does God want intelligent people as worshipers? If God wants worshipers, then God would have to be an imperfect being who wanted worship. Perhaps God wants intelligence because God values the existence of moral beings, and only intelligent beings can have moral worth. It's not clear that only intelligent beings can have moral worth. But, in any case, it's not clear why God would want such beings. Does God want there to be suffering? If death is inevitable, wouldn't it be cruel of God to make sure that beings come into existence who have moral worth only so that they can die. The major unsupported premise is that God would want something like us to exist--otherwise our relative improbability would prove nothing--but we are not capable of predicting what God would want.
In sum, Ross makes two arguments with essentially inconsistent assumptions: the universe is perfectly designed for life yet it is impossible that life could occur in that universe. But each of the two arguments is independently unsound, and, moreover, they both rely on the unsupported claim that God, whose mind we cannot know, would want human-like intelligent beings to exist.