A **Probability** $P$ is a [[Set Function]] that assigns to each event $E$ in a sample space $S$ a real number $P(A) \in [0, 1]$ that represents the likelihood that $A$ occurs. $P$ must satisfy three fundamental axioms: 1. $P(S) = 1$ 2. $P(E) \geq 0$ for all events $E$ 3. $P\!\left(\bigcup_{i=1}^{\infty} E_i\right) = \sum_{i=1}^{\infty} P(E_i)$ for any sequence of [[Mutually Exclusive Events]]. --- > [!question]- Probability of a Fair Die {💡 Example} > What is the probability of rolling an even number on a fair, six-sided die? > > [!answer]- Answer > > $E = \text{even number} = \{2, 4, 6\}$ > > $P(E) = P(\{2, 4, 6\}) = P(\{2\}) + P(\{4\}) + P(\{6\})$ > > $\frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2} = 50\%$