# Lecture 1. D) Probability Space

A probability space is a triple $(S,\mathcal{B},P)$, where $S$ is a sample space, $\mathcal{B}$ is a $\sigma$-algebra of events in $S$, and $P$ is a probability function.
• $S$ is the set of possible singleton events.
• $\mathcal{B}$ is the set of questions we can ask the probability function (like, what is the probability that this and that happens, but not that other thing).
• $P$ maps sets into probabilities.