Conditional probability
SAT glossary · Math
Definition
P(A|B), the probability of A once outcomes without B are discarded. On a two-way table, the condition names the row or column whose total becomes the denominator. P(A|B) ̸= P(B|A) in general.
Conditional probability in plain English
Conditional probability answers a narrower question than regular probability: instead of 'what's the chance of A happening out of everything that could happen,' it asks 'what's the chance of A happening, GIVEN that we already know B happened' — written P(A mid B). You've essentially thrown out every outcome where B didn't happen, and you're only looking within the smaller leftover group. On a two-way table, whatever condition comes after 'given' tells you which row or column total to use as your new denominator — you're no longer dividing by the grand total of everyone, just by the people/things in that specific group. And flipping the condition changes the whole question: P(Amid B) is generally a totally different number from P(Bmid A).
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