Addition rule
SAT glossary · Course Foundations
Definition
P(A or B) = P(A) + P(B) - P(A and B); the subtraction exists because outcomes in both events were counted twice. Whenever an item supplies P(A and B) it is supplying it because you must subtract it — a number given and unused is a number you were supposed to use.
Addition rule in plain English
Imagine two overlapping circles on a Venn diagram, one for event A and one for event B. If you want the probability that A happens OR B happens, you might think 'just add them up' — but if you do that, the overlapping middle part (where both happen at once) gets counted twice, once in each circle. The formula P(A or B) = P(A) + P(B) - P(A and B) fixes that by subtracting the overlap back out once, so it's only counted a single time. That's exactly why, whenever a question hands you the 'both' probability, it's not just extra decoration — it's a piece you're supposed to plug into that subtraction, and forgetting to subtract it is the single most common mistake on these problems.
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