Mutually exclusive events

When talking about probability, if two events are mutually exclusive, it means that both can’t happen. Only one of them.

For example, if we roll a die, the events “rolling a 1” and “rolling a 2” are mutually exclusive. If we roll a 1, we can’t also roll a 2.

On the other hand, “rolling an even nuumber” and “rolling a prime number” are not mutually exclusive, because we can roll a 2, which is both even and prime.

If we draw this as a venn diagram, mutually exclusive events would be two circles that don’t overlap.

If A and B are mutually exclusive events, A and B cannot both occur at the same time.

Probability of mutually exclusive events both happening

Given that the two events can’t happen at the same time, we can write this probability:

P(A \cap B) = 0

flashcards

QuestionAnswer
What are mutually exclusive events?Events where both cannot happen; only one of them can occur.
What is an example of mutually exclusive events when rolling a die?“Rolling a 1” and “rolling a 2” are mutually exclusive, because rolling a 1 means you cannot also roll a 2.
What is an example of events that are not mutually exclusive when rolling a die?“Rolling an even number” and “rolling a prime number” are not mutually exclusive, because rolling a 2 satisfies both conditions.
How are mutually exclusive events represented in a Venn diagram?As two circles that do not overlap.
If A and B are mutually exclusive events, what is the probability P(A \cap B)?P(A \cap B) = 0