Page:Philosophical Transactions - Volume 053.djvu/439

 the proportion of the number of times it will happen, to the number of times it will fail in thoe trials, hould differ les than by mall aligned limits from the proportion of the probability of its happening to the probability of its failing in one ingle trial. But I know of no peron who has hewn how to deduce the olution of the convere problem to this; namely, “the number of times an unknown event has happened and failed being given, to find the chance that the probability of its happening hould lie omewhere between any two named degrees of probability.” What Mr. De Moivre has done therefore cannot be thought ufficient to make the conideration of this point unneceary: epecially, as the rules he has given are not pretended to be rigorouly exact, except on uppofition that the number of trials made are infinite; from whence it is not obvious how large the number of trials mut be in order to make them exact enough to be depended on in practice.

Mr. De Moivre calls the problem he has thus olved, the hardet that can be propoed on the ubjedt of chance. His olution he has applied to a very important purpoe, and thereby hewn that thoe a remuchare much [sic] mitaken who have ininuated that the Doctrine of Chances in mathematics is of trivial conequence, and cannot have a place in any erious enquiry. The purpoe I mean is, to hew what reaon we have for believing that there are in the contitution of things fixt laws according to which events happen, and that, therefore, the frame of the world mut be