Notes on probability

Probability quantifies the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). An experiment has various outcomes, and the set of all possible outcomes is the sample space. An event is a specific collection of outcomes. The probability of an event $A$ is often calculated as:

$$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

Key rules include the Addition Rule for "or" events and the Multiplication Rule for "and" events, especially for independent occurrences.