This chapter begins by providing the general definition of probability and probability space, explaining the roles of sample space, probability measure, and the \(\sigma \) -field of random events, including the construction of an unmeasurable set. Next, it discusses the discrete sample space (classical probability) and the geometric probability (with examples such as Buffon’s needle and Bertrand paradox). Conditional probability (total probability formula, Bayes rule) is introduced and illustrated by the example of the Monty-Hall problem. In the section on independent events, Bernoulli trials and the ”Colorful hat problem” are explored. The optimal strategy of solving it can be described in the Hamming code language and used for error correction in data transmission and to compress data in computer memory). The upper and lower limits of the sequences of the events ( \(\limsup _{n}An\) , \(\liminf _{n}An\) ) and the Borel-Cantelli lemma are discussed at the end of this chapter.