Final answer:
The question is about the concept of mutually exclusive events in a probability experiment. Events are mutually exclusive if they cannot occur at the same time, which means P(E AND F) must equal zero.
Step-by-step explanation:
The question pertains to a probability experiment and determining whether two events, E and F, are mutually exclusive. To answer if events are mutually exclusive, we need to assess if the events can occur simultaneously. If the probability of E and F happening at the same time (P(E AND F)) is zero, then they are considered mutually exclusive.
Mutually Exclusive Events are events that cannot occur at the same time, so their common outcomes are none, and thus P(A AND B) = 0. If event E and event F have no outcomes in common, they are mutually exclusive. For example, if E is the event of flipping a coin and getting a head and F is the event of getting a tail, they are mutually exclusive because they can't happen at the same time.
We can also use tools like Venn diagrams or tree diagrams to visually represent and understand these concepts, as suggested in the provided material. These diagrams can help in seeing the overlap or lack of overlap of events, further clarifying whether they are mutually exclusive.