Which of the following best describes mutually exclusive events?

Mutually exclusive events are defined as events that cannot occur simultaneously; in other words, the occurrence of one event precludes the occurrence of the other. When two or more events are mutually exclusive, they do not share any outcomes in a given sample space, meaning they have no points in common at all.

For instance, if you were to roll a six-sided die, the events of rolling a 2 and rolling a 5 are mutually exclusive because it is impossible to roll both a 2 and a 5 in a single roll. The correct answer accurately captures this definition, establishing that for mutually exclusive events, there are no shared outcomes.

In contrast, other options describe relationships between events that do not fit the definition of mutual exclusivity. For example, the first choice suggests that events can occur at the same time, which contradicts the essence of mutually exclusive events. The second option addresses situations where events might overlap partially, indicating that both events can happen simultaneously. The third choice implies that events can share common outcomes, which also directly opposes the fundamental concept of mutual exclusivity. Thus, the answer distinctly highlighting no common sample points aligns perfectly with the definition of mutually exclusive events.