59

110

now the only remaining possibilities were
at the beginning of our walk
b x b x b x (1-b) and b x b x b x b
and now that there are no other possibilities
the probability of the last man being a baptist
is simply
b⁴/b³ (1-b) + b⁴ = b/(1-b) + b = b
That is, the probability is just what it was in the
first place. If the events are not independent
still the probability of the fourth man being a baptist
must be greater the greater the antecedent probability
of it. Yet the real argument that he will be a baptist
has no force except from the fact that it is a strange
thing to meet three baptists successively. But of course,
to say that the events are independent, precisely
amounts to saying that you cannot argue from one to another.