Page:Chance, love, and logic - philosophical essays (IA chancelovelogicp00peir 0).pdf/138

 wbbb. bwbb. bbwb. bbbw. wbbb. bwbb. bbwb. bbbw. wbbb. bwbb. bbwb. bbbw. wbbb. bwbb. bbwb. bbbw.

bbbb. In the second group, where there is one b, there bbbb. are two sets just alike; in the third there are 4, in bbbb. the fourth 8, and in the fifth 16, doubling every bbbb. time. This is because we have supposed twice as bbbb. many black balls in the granary as white ones; had bbbb. we supposed 10 times as many, instead of bbbb. bbbb. 1, 2,   4,   8,   16 bbbb. bbbb. sets we should have had bbbb. bbbb. 1,  10,   100,   1000,   10000 bbbb. bbbb. sets; on the other hand, had the numbers of black bbbb. and white balls in the granary been even, there bbbb. would have been but one set in each group. Now

suppose two balls were drawn from one of these urns and were found to be both white, what would be the probability of the next one being white? If the two drawn out were the first two put into the urns, and the next to be drawn out were the third put in, then the probability of this third being white would be the same whatever the colors of the first two, for it has been supposed that just the same proportion of urns has the third ball white among those which have the first two white-white, white-black, black-white,