Algebra of logic in theory of events

The article introduces the concept of the binary (Boolean) event. We consider event E defined by Boolean functions E=F(E$_1$, E$_2$, …, E$_n$), in which E$_1$, E$_2$, …, E$_n$ are Boolean events. A theorem on the probability of an event provided by such a formula is proved, and the application of the theorem is shown on the problems. A theorem on the structure of the truth table of the Boolean function E=F(E$_1$, E$_2$, …, E$_n$) is given, in which E$_1$, E$_2$, …, E$_n$ are Boolean events that form exhaustive events. For the events under consideration, the form of the formula for the full probability is obtained, as well as the calculated formulas for the conditional probabilities and the Bayes’ formula. The problems on the application of the obtained formulas are given.