For _is_ the supposition, that the different specified kinds of bags are equally likely, the most reasonable supposition under the circumstances in question? One man may think it is, another may take a contrary view. In fact in an excellent manual[6] upon the subject a totally different supposition is made, at any rate in one example; it is taken for granted in that instance, not that every possible number of black and white balls respectively is equally likely, but that every possible way of getting each number is equally likely, whence it follows that bags with an intermediate number of black and white balls are far more likely than those with an extreme number of either. On this supposition five black and five white being obtainable in 252 ways against the ten ways of obtaining one white and nine black, it follows that the chance that we have drawn from a bag of the latter description is much less than on the hypothesis first made. The chance, in fact, becomes now 1/512 instead of 1/55. In the one case each distinct result is considered equally likely, in the other every distinct way of getting each result. 14. Uncertainties of this kind are peculiarly likely to arise in these inverse probabilities, because when we are merely given an effect and told to look out for the chance of some assigned cause, we are often given no clue as to the relative prevalence of these causes, but are left to determine them on general principles. Give us either their actual prevalence in statistics, or the conditions by which such prevalence is brought about, and we know what to do; but without the help of such data we are reduced to guessing. In the above example, if we had been told how the bag had been originally filled, that is by what process, or under what circumstances, we should have known what to do. If it had been filled at random from a box containing equal numbers of black and white balls, the supposition in Mr Whitworth's example is the most reasonable; but in the absence of any such information as this we are entirely in the dark, and the supposition made in §12 is neither more nor less trustworthy and reasonable than many others, though it doubtless possesses the merit of superior simplicity.[7] If the reader will recur to Ch. V. §§4, 5, he will find this particular difficulty fully explained. Everybody practically admits that a certain characteristic arrangement or distribution has to be introduced at some prior stage; and that, as soon as this stage has been selected, there are no further theoretic difficulties to be encountered. But when we come to decide, in examples of the class in question, at what stage it is most reasonable to make our postulate, we are often left without any very definite or rational guidance.