To determine the relationship between events A and B, we need to analyze them based on their definitions:
- Event A: The student is a man.
- Event B: The student belongs to a sorority.
Mutually Exclusive:
Two events are mutually exclusive if they cannot occur at the same time. In this case, a student cannot be both a man and a member of a sorority simultaneously (assuming traditional definitions of sororities as female-only organizations). Hence, events A and B are mutually exclusive.
Independent:
Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. Given that a man cannot belong to a sorority, the occurrence of event A (a student being a man) directly affects the likelihood of event B (the student belonging to a sorority) because if event A occurs, event B cannot occur. Therefore, they are not independent.
Conclusion:
Events A and B are mutually exclusive.