Question

Determine whether the following events are mutually exclusive. Explain your reasoning.

Event A: Randomly select a female communications major.
Event B: Randomly select a communications major who is 21 years old.
These events____mutually exclusive, since____
a. >every male mathematics major is 19 years old.
b. it is not possible to select a male mathematics major who is 19 years old.
c. no mathematics majors are male.
d. it is possible to select a male mathematics major who is 19 years old.
e. all mathematics majors are male.
f. not all mathematics majors are male.
g. not every male mathematics major is 19 years old.

Answer 1

Events A and B are not mutually exclusive because it is possible for a student to be a female communications major and 21 years old at the same time. The misunderstanding in the question stems from irrelevant examples that do not match the events described. The correct option explaining why they are not mutually exclusive is (d).

Step-by-step explanation:

To determine whether the events A and B are mutually exclusive, we need to understand whether these two events can occur at the same time. By definition, mutually exclusive events are events that cannot happen at the same time (i.e., the probability of both events occurring simultaneously is zero).

Event A is 'Randomly select a female communications major.' Event B is 'Randomly select a communications major who is 21 years old.' These events are not mutually exclusive because it is possible for a student to be both a female communications major and 21 years old simultaneously. Therefore, a student who fits both criteria could be selected, meaning that the occurrence of Event A does not preclude the occurrence of Event B, and vice versa.

The correct option that explains why these events are not mutually exclusive is (d) it is possible to select a male mathematics major who is 19 years old. Please note that while option (d) uses the example of a male mathematics major being 19, it aligns with our context by illustrating a scenario where two events can coexist, which is analogous to a female communications major being 21 years old.