Whenever probability is being considered there must be some type of relevant or total background information (usually depicted as k). The immediate objection when applying a probability rule or calculus to the fine-tuning of the universe in a multiverse scenario would be to say that this is universe is not an appropriate random sampling. In other words, if we know of [at least] only one universe with these values the random sample size is precisely 1; thus, no random sample can be used to assess the probability of certain values of physics in the argument. In statistics a random sample drawn must have the same chance of being sampled as all the other samples. Since we know of only one universe we do not know what the range of values for the constants and physics could be. Additionally, since we don’t know how narrow or broad these ranges could be there’s no way of drawing out any probability based argument for fine-tuning. However, we can know what other universes would be like if the values were different. If our natural laws have counterfactuals that are in any way incoherent then this is an appropriate sampling. Also, to make this objection and advocate that we just so happen to live in a life permitting universe in the multiverse then this objection cannot be made since the claim that we happen to life in a life-permitting one amongst countless others suggest we can know what the other samplings are. For instance, if the strong nuclear force were any stronger the universe would be composed of only hydrogen and if gravity were any weaker stars could never form to create the heavier elements. If these counterfactuals make any coherent sense and are possible then we can draw an appropriate random sample. Also, note that we do not have to know how narrow or broad the range of values could be. That does not matter. It could be very narrow or extremely broad and this sampling still is appropriate.[i] Thus, by virtue of the possible counterfactual expressions of the values of the constants and laws of nature I believe we can make an appropriate probability based calculation.
The role probability serves in this argument does not favor the non-fine-tuning hypothesis (either chance, necessity, or a combination of the sort) in multiverse scenarios. If the objector to a fine-tuner argues that the odds of having a finely tuned universe, which harbors life, increases given the vast number of universes there is bound to be one with the values we have. This is an abuse of probability and commits the gambler’s fallacy. This claim assumes a general disjunction rule of probability. For example, this rule of probability suggests that the probability of drawing a king from a deck of cards increases when each card drawn is not replaced. If the deck has all the cards it is supposed to have the probability of eventually drawing a king is 1. The multiverse is like the restricted or general conjunction rule of probability. By simply increasing the number of possibilities does not increase the probability of selection. For example, say you randomly draw a card from the deck and you want the king of spades. The odds of you drawing a king of spades are 1/52. Say you draw the three of hearts. When you replace the card and draw another card from random the odds of you getting the king of spades is not increased by the first selection.
[i] What may be argued for is the mechanism that produces these random constants. This mechanism would be superstring theory or M-theory. Even though there may be a huge number of possible universes lying within the life-permitting universe, region of the cosmic landscape, nevertheless that life-permitting region will be unfathomably tiny compared to the entire landscape. This also shows that the physical universe itself is not unique. The physical universe does not have to be the way it is: it could be been otherwise functioning under different laws. Paul Davies, The Mind of God (New York: Simon & Schulster, 1992), 169. Davies means the laws of physics within the actual values of the constants, not confusing there being different values of the constants with there being different laws.