Probability Basics

Probability quantifies the likelihood of events, a key concept in statistics, gaming, and decision-making.

Definition

For an event \( A \), probability is:

\( P(A) \) ranges from 0 (impossible) to 1 (certain).

Example: Rolling a Die

Possible outcomes: {1, 2, 3, 4, 5, 6}. Probability of rolling a 6:

Graphical View

Uniform probability for a fair die:

Rules

Addition Rule: For mutually exclusive events, \( P(A \text{ or } B) = P(A) + P(B) \). E.g., \( P(1 \text{ or } 2) = \frac{1}{6} + \frac{1}{6} = \frac{1}{3} \).

Complement: \( P(\text{not } A) = 1 - P(A) \). E.g., \( P(\text{not 6}) = 1 - \frac{1}{6} = \frac{5}{6} \).

Applications

Probability predicts weather, assesses risks in insurance, and underpins machine learning models.