What is the definition of mutually exclusive events?

Conditions

• Events A and B are two events in the same random experiment.

Reasoning, step by step

1. Identify the intersection of events A and B, denoted as AB.
2. Check if the intersection is the empty set ($AB = \emptyset$).
3. Conclude that if $AB = \emptyset$, the events are mutually exclusive and cannot happen at the same time.

Example

In a single coin toss, the event of getting heads and the event of getting tails are mutually exclusive because their intersection is the empty set ($AB = \emptyset$).

Common misconceptions

• Confusing mutually exclusive events with independent events.
• Assuming that mutually exclusive events can occur at the same time under certain conditions.

Watch the explanation

Explore next

• Why are mutually exclusive events with nonzero probabilities generally not independent?
• Are impossible events independent of any event?