- ing the different possibilities, which, on the application of
this principle, would give different results. If there be any way of enumerating the possibilities so as to make them all equal, it is not that from which this solution is derived, but is the following: Suppose we had an immense granary filled with black and white balls well mixed up; and suppose each urn were filled by taking a fixed number of balls from this granary quite at random. The relative number of white balls in the granary might be anything, say one in three. Then in one-third of the urns the first ball would be white, and in two-thirds black. In one-third of those urns of which the first ball was white, and also in one-third of those in which the first ball was black, the second ball would be white. In this way, we should have a distribution like that shown in the following table, where w stands for a white ball and b for a black one. The reader can, if he chooses, verify the table for himself.
wwww.
wwwb. wwbw. wbww. bwww.
wwwb. wwbw. wbww. bwww.
wwbb. wbwb. bwwb. wbbw. bwbw. bbww.
wwbb. wbwb. bwwb. wbbw. bwbw. bbww.
wwbb. wbwb. bwwb. wbbw. bwbw. bbww.
wwbb. wbwb. bwwb. wbbw. bwbw. bbww.
wbbb. bwbb. bbwb. bbbw.
wbbb. bwbb. bbwb. bbbw.
wbbb. bwbb. bbwb. bbbw.
wbbb. bwbb. bbwb. bbbw.
