1. The problem asks to explain the terms "mutually exclusive events" and "independent events" in probability. 2. **Mutually exclusive events** are events that cannot happen at the same time. If event A occurs, event B cannot occur, and vice versa. 3. The formula for mutually exclusive events is: $$P(A \cap B) = 0$$ which means the probability of both A and B happening together is zero. 4. For example, when flipping a coin, the events "getting heads" and "getting tails" are mutually exclusive because you cannot get both outcomes in one flip. 5. **Independent events** are events where the occurrence of one does not affect the probability of the other. 6. The formula for independent events is: $$P(A \cap B) = P(A) \times P(B)$$ which means the probability of both A and B happening together is the product of their individual probabilities. 7. For example, rolling a die and flipping a coin are independent events because the result of the die does not affect the coin flip. 8. To summarize: - Mutually exclusive: events cannot happen together. - Independent: events do not influence each other. This explanation helps understand how to calculate probabilities in different scenarios.