Final answer:
Two mutually exclusive events cannot occur at the same time, with P(A AND B) being zero. Examples include different sides of a die or different faces of a coin toss, which cannot be displayed simultaneously, making such events mutually exclusive.
Step-by-step explanation:
Two mutually exclusive events are events that cannot occur at the same time. According to the definition, if Events A and B are mutually exclusive, then the probability of both A and B occurring at the same time, represented as P(A AND B), is zero. The idea of mutually exclusive events is an important concept in probability theory and statistics.
For example, when tossing a fair die, if Event A is the die showing a 3, and Event B is the die showing a 5, these two events are mutually exclusive because the die cannot show both a 3 and a 5 at the same time. Therefore, P(A AND B) = 0. Similarly, if Event C is the outcome where a coin lands heads, and Event D is the outcome where the same coin toss results in tails, C and D are also mutually exclusive, as a coin cannot land on both sides simultaneously.
In the context of multiple events, such as selecting a card of a certain color followed by a coin toss, Events A and B would be considered mutually exclusive if they represent outcomes that cannot both happen. For instance, if Event A is picking a blue card and then getting heads, and Event B is picking either a red or green card and then getting heads, A and B are mutually exclusive, since a single card cannot be both blue and red or green at the same time.