When are two events A and B said to be mutually exclusive?

When are two events A and B said to be mutually exclusive?

• A. When one event affects the probability of the other
• B. When both can occur at the same time
• C. When they cannot happen at the same time
• D. When their probabilities are equal

Answer: (C)

Two events A and B are termed mutually exclusive when the occurrence of one event means that the other cannot occur. This implies that if event A happens, event B cannot happen at the same time, and vice versa. For example, when flipping a coin, the results 'heads' and 'tails' are mutually exclusive since if the coin shows 'heads', it cannot show 'tails' at that moment. Understanding mutual exclusivity is important in probability theory because it helps in calculating the probabilities of compound events. For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This concept is foundational in various applications of probability in real-world scenarios, making it clear why the choice that states they cannot happen at the same time is indeed the correct one.

Two events A and B are termed mutually exclusive when the occurrence of one event means that the other cannot occur. This implies that if event A happens, event B cannot happen at the same time, and vice versa. For example, when flipping a coin, the results 'heads' and 'tails' are mutually exclusive since if the coin shows 'heads', it cannot show 'tails' at that moment.

Understanding mutual exclusivity is important in probability theory because it helps in calculating the probabilities of compound events. For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities. This concept is foundational in various applications of probability in real-world scenarios, making it clear why the choice that states they cannot happen at the same time is indeed the correct one.