Final answer:
Event A (selecting a female history major) and Event B (selecting a history major who is 19 years old) are not mutually exclusive because it is possible for an individual to fulfill both criteria at the same time, thus P(A AND B) is not zero.
Step-by-step explanation:
To determine whether two events are mutually exclusive, we must assess whether they can occur at the same time.
By definition, mutually exclusive events cannot occur simultaneously, which means the probability of both events happening at the same time (P(A AND B)) is equal to zero. In the context of the question, Event A is randomly selecting a female history major, and Event B is randomly selecting a history major who is 19 years old.
It is possible for a female history major to be 19 years old, so there is an overlap between the two events. Therefore, these events are not mutually exclusive.
If a student is a 19-year-old female history major, they would be counted in both Event A and Event B, which indicates that P(A AND B) is not equal to zero. Since the definition of mutually exclusive requires that P(A AND B) equals zero, these two events cannot be considered mutually exclusive.