Can events be mutually exclusive and independent?
Understand the Problem
The question is asking whether events can be both mutually exclusive and independent at the same time. It's exploring a concept in probability theory regarding the relationship between two types of event interactions.
Answer
No, events cannot be mutually exclusive and independent simultaneously unless one or both events have a probability of zero.
Events cannot be both mutually exclusive and independent unless one or both events have a probability of zero.
Answer for screen readers
Events cannot be both mutually exclusive and independent unless one or both events have a probability of zero.
More Information
Mutually exclusive events cannot occur together, while independent events do not influence each other. The conditions for these characteristics naturally conflict.
Tips
A common mistake is confusing the definitions of mutually exclusive and independent events. Another mistake is not considering the zero probability condition.
