What does the formula P(A ∩ B) = 0 indicate?

What does the formula P(A ∩ B) = 0 indicate?

• A. Events A and B are independent
• B. Events A and B are never supposed to happen
• C. Events A and B are mutually exclusive
• D. Events A and B always happen together

Answer: (C)

The formula P(A ∩ B) = 0 signifies that the probability of both events A and B occurring simultaneously is zero. This indicates that if one event occurs, the other cannot happen at the same time. This situation is characteristic of mutually exclusive events. When events are mutually exclusive, the occurrence of one event excludes the possibility of the other event occurring, leading to a probability of intersection that equals zero. In contrast, if events were independent, it would be possible for both A and B to happen, and the intersection would not be zero. Therefore, the manifestation of an intersection probability of zero confirms that events A and B are mutually exclusive.

The formula P(A ∩ B) = 0 signifies that the probability of both events A and B occurring simultaneously is zero. This indicates that if one event occurs, the other cannot happen at the same time. This situation is characteristic of mutually exclusive events. When events are mutually exclusive, the occurrence of one event excludes the possibility of the other event occurring, leading to a probability of intersection that equals zero.

In contrast, if events were independent, it would be possible for both A and B to happen, and the intersection would not be zero. Therefore, the manifestation of an intersection probability of zero confirms that events A and B are mutually exclusive.