## Definition ==Probability== is a set function $P$ that assigns to each event $A$ in a sample space $S$ a real number $P(A) \in [0, 1]$ representing the likelihood that $A$ occurs. It must satisfy the axioms: $P(S) = 1$, $P(A) \geq 0$ for all events $A$, and $P\!\left(\bigcup_{i=1}^{\infty} A_i\right) = \sum_{i=1}^{\infty} P(A_i)$ for any sequence of mutually exclusive events. > [!example]- A jar contains 3 red, 5 blue, and 2 green marbles. What is the probability of drawing a blue marble? > There are $3 + 5 + 2 = 10$ equally likely outcomes. The event "blue" contains 5 outcomes, so > $ P(\text{blue}) = \frac{5}{10} = 0.5 $