We have been discussing some of the fundamental features of the classical calculus of probability. The equiprobability of rival events was seen to be a major assumption of the calculus. Moreover, it is an assumption which the pure mathematician need not bother to justify. He need only present his formal system as follows: If all the alternatives are equiprobable, then my system provides the complete machinery for calculating the probability of alternative events occurring. But whether actual alternatives, say in a laboratory experiment, are equiprobable is not for the pure mathematician to say. He is concerned only to work out the consequences of a system based upon that assumption.