What is the probability P(A∩B) when A and B are mutually exclusive?

What is the probability P(A∩B) when A and B are mutually exclusive?

• A. 1
• B. 0
• C. 0.5
• D. Depends on the events

Answer: (B)

In probability theory, when two events are described as mutually exclusive, it means that they cannot happen at the same time. If event A occurs, event B cannot occur, and vice versa. Therefore, the intersection of these two events, denoted as P(A∩B), represents the probability that both events occur simultaneously. Since A and B cannot happen at the same time, the probability of both events occurring together is zero. Thus, P(A∩B) equals 0. This concept is fundamental in probability, highlighting the relationship between complementary events where the occurrence of one excludes the possibility of the other. Given that P(A∩B) is the case of mutually exclusive events, the only logical conclusion is that the probability is indeed 0. This fits perfectly with the definition of mutually exclusive events, solidifying the understanding of how probabilities work in this context.

In probability theory, when two events are described as mutually exclusive, it means that they cannot happen at the same time. If event A occurs, event B cannot occur, and vice versa. Therefore, the intersection of these two events, denoted as P(A∩B), represents the probability that both events occur simultaneously.

Since A and B cannot happen at the same time, the probability of both events occurring together is zero. Thus, P(A∩B) equals 0. This concept is fundamental in probability, highlighting the relationship between complementary events where the occurrence of one excludes the possibility of the other.

Given that P(A∩B) is the case of mutually exclusive events, the only logical conclusion is that the probability is indeed 0. This fits perfectly with the definition of mutually exclusive events, solidifying the understanding of how probabilities work in this context.