The first premise of Swinburne’s case for God makes a fairly modest claim:
1. Based on evidence other than religious experience, the existence of God is not very improbable.
Because the expression “not very improbable” is a bit vague, I argued for the following clarification of premise (1), in my last post:
1b. Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge: P (h I e & k) > .20

In Swinburne’s estimation, the relevant evidence (other than the evidence from religious experience) makes the probability of God’s existence significantly
…all that my conclusion so far amounts to is that it is something like as probable as not that theism is true, on the evidence so far considered. However, so far in this chapter I have ignored one crucial piece of evidence, the evidence from religious experience. (EOG, 2nd ed., p.341)
In other words, according to Swinburne:
P(h I e & k) ≈ .50
This is where e is the relevant evidence other than religious experience.
Since this is only an approximation, we could consider Swinburne to be correct if the actual probability were somewhere from .40 to .60:
(4) Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge: .40 ≤ P(h I e & k) ≤ .60
Clearly, (4) implies (1b), becuase if the probability of h is between .40 and .60, then the probability of h is greater than .20.
In EOG, Swinburne considers eleven arguments on the question of the existence of God. The first premise of Swinburne’s case for God is concerned with ten of the arguments, and excludes the final argument that is based on religious experience. Two of the ten arguments are set aside as having no significant force, leaving eight arguments to use as the basis for showing that the probability of God’s existence is between .40 and .60.
Seven of the eight remaining arguments are supposed to provide some confirmation of the existence of God, while one argument (the problem of evil) is supposed to provide some disconfirmation of the existence of God. Since each of the arguments that confirm the existence of God is supposed to bump up the probability a bit, so that the cumulative force of the arguments is greater than that of any one particular argument, the claim that Swinburne has to make for each of the confirming arguments is very modest.
Suppose that the problem of evil is only strong enough to cancel out the weight of one of the seven confirming arguments. That would leave six confirming arguments to support the cumulative probability of between .40 and .60.
If we assume that the prior probability of the existence of God was equal to one chance in a hundred, i.e. P(h I k) = .01, and if we assume that each of the six remaining confirming arguments bumps up the probability by the same amount (on average), then the probability of h would seven times .01:
P (h I e & k) = 7 x .01 = .07
On this scenario, Swinburne’s claim that the probability of h (given the relevant evidence other than religious experience) was between .40 and .60 would clearly be false, as would the weaker claim made in premise (1b), namely that h was greater than (or equal to) .20.
However, suppose that the prior probability of the existence of God was a bit higher: .05, and suppose that each of the six confirming arguments (remaining after cancelling out one of the confirming arguments with the problem of evil) added .05 to the probability (on average). In that case, the probability of h would be seven times .05:
P (h I e & k) = 7 x .05 = .35
On this scenario, Swinburne’s stronger claim (4) would be false, but this would still be enough to establish his first premise (1b), because a probability of .35 is greater than a probability of .20.
If we were to assume that the prior probability of h was .06, and that each of the six confirming arguments (remaining after the problem of evil cancelled out one confirming argument) bumped up the probability by .06, then not only would premise (1b) be true, but so would Swinburne’s stronger claim:
P (h I e & k) = 7 x .06 = .42
These different scenarios make two important points. First, Swinburne only needs to establish fairly weak claims about the force of his confirming arguments. If each confirming argument bumps up the probability of the existence of God just a bit (say .04 or .05) that may well be sufficient to establish the first premise of his case for God (if force of the problem of evil is only about the same as one of the confirming arguments, and if there is at least a tiny prior probability of the existence of God).
Second, the difference between success and failure is small, now that we have clarified the probability required to make the first premise true. If the average bump up of probability by the confirming arguments (and the prior probability of God’s existence) is .02 (i.e., two chances in a hundred), then premise (1b) is likely to be false, but if the average bump up of probability by the confirming arguments (and the prior probability of God’s existence) is .03 (i.e. three chances in a hundred), then premise (1b) is likely to be true (depending on the force of the problem of evil in disconfirming God’s existence).
greater than .20: