Union of Events & the Addition Rule
Compute P(A ∪ B) using the addition rule:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Use probabilities, a 2×2 table, or a two-person (two-trial) tree diagram.
Union of Events and the Addition Rule
Statistics • Probability
Frequently Asked Questions
What is the union of two events in probability?
The union A ∪ B means event A happens, or event B happens, or both happen. It represents the probability of at least one of the two events occurring.
How do you calculate P(A or B) with the addition rule?
Use P(A ∪ B) = P(A) + P(B) - P(A ∩ B). The intersection is subtracted once because outcomes in A ∩ B are counted twice when you add P(A) and P(B).
When can I use P(A ∪ B) = P(A) + P(B)?
You can use that simplified rule when events are mutually exclusive, meaning they cannot occur together. In that case P(A ∩ B) = 0, so the subtraction term disappears.
How do I find the union probability from a 2x2 table of counts?
Compute Count(A ∪ B) = Count(A) + Count(B) - Count(A ∩ B), then divide by the total N to convert counts to probabilities. The A ∩ B term is the cell where both categories occur.