Rules of Probability

Probability is governed by a few foundational rules.

First, probabilities are always between \( 0 \) and \( 1 \) (non-negativity).

Second, the probability of the entire sample space is \( 1 \) (normalization).

Third, if two events cannot happen at the same time (i.e., are mutually exclusive), the probability of either occurring is the sum of their individual probabilities (additivity).

Other useful rules include:

- The addition rule for non-mutually exclusive events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

- The complement rule: \[ P(\text{not } A) = 1 - P(A) \]

- The multiplication rule for independent events: \[ P(A \cap B) = P(A) \times P(B) \]

Knowing these rules by heart is essential for solving complex probability problems, especially in the context of trading interviews.