popper-logic-scientific-discovery

APPENDIX *iii
On the Heuristic Use of the Classical
Definition of Probability, Especially
for Deriving the General
Multiplication Theorem
The classical definition of probability as the number of favourable cases
divided by the number of equally possible cases has considerable heuristic
value. Its main drawback is that it is applicable to homogeneous or
symmetrical dice, say, but not to biased dice; or in other words, that it
does not make room for unequal weights of the possible cases. But in some
special cases there are ways and means of getting over this difficulty;
and it is in these cases that the old definition has its heuristic value:
every satisfactory definition will have to agree with the old definition
where the difficulty of assigning weights can be overcome, and therefore,
a fortiori, in those cases in which the old definition turns out to be
applicable.
(1) The classical definition will be applicable in all cases in
which we conjecture that we are faced with equal weights, or equal
possibilities, and therefore with equal probabilities.
(2) It will be applicable in all cases in which we can transform
our problem so as to obtain equal weights or possibilities or
probabilities.