Each of these explanations accounts for the fact that the disciples in Papias's prologue are named in the same order in which they appear in John by postulating that Papias was familiar with John and was consciously dependent on the Gospel in constructing the list of disciples in his prologue. Since no one has proposed that John might be dependent on Papias or that their agreement is due to reliance on a hypothetical common source, the only realistic alternative is to postulate that the correspondence is simply fortuitous. Although Bauckham writes that the correspondence is unlikely to be coincidental, judgments about what is or is not coincidental can be rather subjective. In this case, however, there is a simple statistical principle that can add greater objectivity to Bauckham's statement.
In an effort to discover the quantifiable probability that this correspondence is by chance, I consulted with Kevin Carlin, a mathematician with a doctorate from Yale University. He confirmed that if it is given that Papias and John are each going to name the same six disciples (i.e., if we take it for granted that they are going to name the same six disciples), then, on the basis of the conditional probability theorem, the probability that each will name the same disciples in the same order is 720:1. In other words, the odds are 99.86 percent (719/720) that the correspondence is not by chance. …
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