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
| Question | Answer |
|---|---|
| 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 |