Question

determine whether the following events are mutually exclusive. explain your reasoning.
event a: randomly select a female physics major.
event b: randomly select a physics major who is 22 years old.

these events mutually exclusive, since

• it is not possible to select a female physics major who is 22 years old.
• not every female physics major is 22 years old.
• not all physics majors are female.
• no physics majors are female.
• it is possible to select a female physics major who is 22 years old.
• every female physics major is 22 years old.
• all physics majors are female.

Explanation:

Define mutually exclusive events

Using the Mutually Exclusive Events knowledge point
Two events are mutually exclusive if they cannot occur at the same time. Mathematically, this means their intersection is empty:

$$ P(A \cap B) = 0 $$

Analyze the given events

Using the Mutually Exclusive Events knowledge point

• Event A: Randomly select a female physics major.
• Event B: Randomly select a physics major who is 22 years old.

To determine if they are mutually exclusive, we check if a single selected person can satisfy both conditions simultaneously. A person who is a female physics major and is 22 years old satisfies both Event A and Event B. Since such a person can exist, the events can occur at the same time. Therefore, the events are not mutually exclusive.

Answer:

These events <blank>are not</blank> mutually exclusive, since <blank>it is possible to select a female physics major who is 22 years old.</blank>