1. The problem is to explain key terms under probability. 2. Probability is the measure of how likely an event is to occur, expressed as a number between 0 and 1. 3. Important terms: - **Experiment:** A process or action that results in one or more outcomes. - **Sample Space ($S$):** The set of all possible outcomes of an experiment. - **Event ($E$):** A subset of the sample space; one or more outcomes. - **Probability of an event ($P(E)$):** The likelihood that event $E$ occurs, calculated as $$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes in } S}$$ - **Complement of an event ($E^c$):** The event that $E$ does not occur, with probability $$P(E^c) = 1 - P(E)$$ - **Mutually exclusive events:** Events that cannot happen at the same time, so $$P(A \cap B) = 0$$ - **Independent events:** Events where the occurrence of one does not affect the probability of the other, so $$P(A \cap B) = P(A) \times P(B)$$ 4. These terms form the foundation for understanding and calculating probabilities in various contexts.