Recurrent formation of discrete probabilistic distributions of random sets of events

The class of discrete probabilistic distributions of the II type of a random set on a set of $N$ events is investigated. For constructing such probabilistic distributions, a recurrent formula and associative functions are offered to use. The advantage of the approach is that for the definition of the probabilistic distribution, instead of $2^N$ probabilities of events, it is enough to know $N$ probabilities and the type of the associative function. This approach is tested for some three associative functions. The theorems establishing their forms and the legitimacy conditions for obtained probabilistic distributions of random sets of events are proven.