Module 2 · Probability Foundations · Topic 3
Complement. The complement of event A, written A′ (or Ā), is the event that A does not occur. Together, A and A′ account for all possible outcomes.
P(A′) = 1 − P(A)
P(A | B) = P(A and B) / P(B) — Probability of A after restricting attention to cases where B occurred.P(A | B) = P(B | A)P(A) / P(B) — Updates a prior probability after observing evidence.If P(rain tomorrow) = 0.35, then P(no rain) = 1 − 0.35 = 0.65.
The complement rule is especially useful when computing P(A) directly is hard. For “at least one” problems, compute 1 − P(none) instead.
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