Mutually Exclusive Events and Unions of Events

What are mutually exclusive events?

Events that cannot happen at the same time. If one occurs, the other cannot.

What is an example of mutually exclusive events

Flipping a coin: getting heads and tails at the same time is impossible

What’s the formula for the probability of mutually exclusive events A or B happening?

P(A or B) = P(A) + P(B)

What does it mean if events are not mutually exclusive?

They can happen at the same time — they can overlap

What’s the formula for the probability of any two events A or B happening?

P(A or B) = P(A) + P(B) - P(A and B)

Why do we subtract P(A and B) in the formula

To avoid double-counting the overlap when A and B are not mutually exclusive.

If events A and B are mutually exclusive, what is P(A and B)

P(A and B) = 0, because both can’t happen together.

What does the word “union” in probability mean?

It means either event A happens, or event B happens, or both. Written as P(A ∪ B)

∪

• or

• • At least one happens (A or B or both)

∩

• AND

• Both happen (A and B)