Addition Rule
Probability that A or B occurs.
Formula
Variables
Example
For mutually exclusive events the last term is 0
How it works
The union A B means every outcome that is in A, in B, or in both. If you add P(A) and P(B) directly, the overlap is counted twice, so you subtract P(A \cap B) once to correct for that double-counting. This is why the rule works whether the events are independent, dependent, or mutually exclusive.
When to use it
Use this formula whenever a question asks for the probability that at least one of two events happens. It is especially useful in survey, card, dice, quality-control, and medical-testing problems where events can overlap.
Worked example, step by step
A school survey finds that 40% of students play basketball (A), 25% play soccer (B), and 10% play both. P(A \cup B) = P(A) + P(B) - P(A \cap B) P(A \cup B) = 0.40 + 0.25 - 0.10 P(A \cup B) = 0.55 So, the probability that a student plays basketball or soccer is 0.55, or 55%.
Common mistakes to avoid
- Adding P(A) and P(B) without subtracting the overlap
- Using the formula for "and" instead of "or"
- Assuming the events must be mutually exclusive before applying the rule
Did You Know?
Subtracting the intersection avoids double-counting.
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