ABSTRACT
For higher degrees of probability we must turn to another form of inference which starts from a very simple idea. If you throw a die, and know of no reason why it should fall with any one side uppermost rather than any other, then the chances are said to favour each of the sides equally. Hence that fall which brings the ace uppermost represents only one out of six cases, all of which are equally possible. Hence the probability of the ace turning up is said to be 1/6 of the whole range of probabilities. Now, if we take the fact that the die will fall as certain, and represent certainty by 1, the probability of an ace will be represented by the fraction 1/6 (there being six equally possible ways in which the certain event may take place). From this assumption follow the whole mathematics of chance. If we throw two dice (instead of one), there are thirty-six possible combinations, and hence the chance of aces is 1/36. On the other hand, there are six ways in which we may throw doubles, and hence the chance of such a throw is 6/36 = 1/6. Thus the rule is that the probability of any event is to be expressed by a fraction in which the numerator gives the number of known contingencies in which the event will take place, and the denominator the total number of equally possible alternatives. Now our question is, What does the original assumption mean? What is meant by saying that the chances are equal, or that the probability of one event M is 1/6 and that of another N 35/36?
