Probability — Formula Sheet

P(E|F) = P(E ∩ F) / P(F), P(F) ≠ 0

P((A ∪ B)|F) = P(A|F) + P(B|F) - P((A ∩ B)|F)

P(E'|F) = 1 - P(E|F)

P(E ∩ F ∩ G) = P(E) P(F|E) P(G|EF)

P(F|E) = P(F) and P(E|F) = P(E)

P(E ∩ F) = P(E) · P(F)

P(E ∩ F) ≠ P(E) · P(F)

P(A ∩ B) = P(A)P(B) for every pair of events from two experiments

P(A ∩ B) = P(A)P(B), P(A ∩ C) = P(A)P(C), P(B ∩ C) = P(B)P(C), and P(A ∩ B ∩ C) = P(A)P(B)P(C)

The probability of event E given that event F has already occurred is P(E|F)=P(E∩F)/P(F), provided P(F)≠0.

For any event F with P(F)≠0, P(S|F)=1, P(E'|F)=1-P(E|F), and P((A∪B)|F)=P(A|F)+P(B|F)-P((A∩B)|F).

For two events, P(E∩F)=P(E)·P(F|E)=P(F)·P(E|F), provided P(E)≠0 and P(F)≠0.