CS 229 - Probabilities and Statistics refresher

Sample space The set of all possible outcomes of an experiment is known as the sample space of the experiment and is denoted by $S$. Event Any subset $E$ of the sample space is known as an event. That is, an event is a set consisting of possible outcomes of the experiment. If the outcome of the experiment is contained in $E$, then we say that $E$ has occurred. Axiom 1 ― Every probability is between 0 and 1 included, i.e: Axiom 2 ― The probability that at least one of the elementary events in the entire sample space will occur is 1, i.e: Axiom 3 ― For any sequence of mutually exclusive events $E_1, ..., E_n$, we have: Permutation A permutation is an arrangement of $r$ objects from a pool of $n$ objects, in a given order.