When we talk about two events being mutually exclusive, we mean that they cannot occur at the same time. In other words, if one event happens, the other cannot happen simultaneously. This is a fundamental concept in probability theory.
To put it simply, if you have two events, say Event A and Event B, and they are mutually exclusive, the probability of both events occurring at the same time is calculated as follows:
P(A and B) = 0
This indicates that the probability of both events happening together is zero. Since one event’s occurrence precludes the other’s occurrence, they cannot overlap. For example, consider the events of rolling a die: if we define Event A as rolling an even number (2, 4, or 6) and Event B as rolling an odd number (1, 3, or 5), these events are mutually exclusive. If you roll the die, it cannot land on an even number and an odd number simultaneously.
In summary, the key takeaway is that if two events are mutually exclusive, the probability that both events occur at the same time is 0.