Graduate School of
Science and Engineering

If the “result” that can be obtained is limited (two sides of a coin toss or the throw of a dice etc) the probability of each “result” primarily considered, however, the obtainable “result” will be non-countable and unlimited, in that the probability of each “result” in the limited case results in a contrariety, even if a value could be set for the probability. 

Modern probability theory resolves this dilemma by abstracting the concept and measuring the size, thus enabling probability that is non-countable and has unlimited “results” to be considered. However, that abstraction does result in a new dilemma: the existence of an assembly for which the size cannot be measured. 

As revealed above probability theory is an interesting research subject. It is also an interesting mathematical field that has the aspect of being actually applicable in various parts in society by being linked to statistical methods.