概率论的基本公式

A⊂B,P(B−A)=P(B)−P(A)A \subset B,P(B-A)=P(B)-P(A) P(A∪B)=P(A)+P(B)−P(AB)P(A \cup B) = P(A) + P(B) -P(AB) P(A1∪A2∪A3)=P(A1)+P(A2)+P(A3)−P(A1A2)−P(A1A3)−P(A2A3)+P(A1A2A3)P(A_1 \cup A_2 \cup A_3) = P(A_1) + P(A_2) + P(A_3) - P(A_1A_2) - P(A_1A_3) - P(A_2A_3) + P(A_1A_2A_3) P(A1∪A2∪A3∪A4)=P(A1)+P(A2)+P(A3)+P(A4)−[P(A1A2)+P(A1A3)+P(A1A4)+P(A2A3)+P(A2A4)+P(A3A4)]+[P(A1A2A3)+P(A1A2A4)+P(A1A3A4)+P(A2A3A4)]+P(A1A2A3A4)P(A_1 \cup A_2 \cup A_3 \cup A_4) = P(A_1) + P(A_2) + P(A_3) + P(A_4) - [ P(A_1A_2) + P(A_1A_3) + P(A_1A_4) + P(A_2A_3) + P(A_2A_4) + P(A_3A_4) ] + [ P(A_1A_2A_3) + P(A_1A_2A_4) + P(A_1A_3A_4) + P(A_2A_3A_4) ] + P(A_1A_2A_3A_4) P(A−B)=P(A)−P(AB)=P(ABˉ)P(A-B) = P(A) - P(AB) = P(A\bar{B}) P(B∣A)=P(AB)P(A)P(B|A) = \frac{P(AB)}{P(A)} P(Bˉ∣A)=1−P(B∣A)P(\bar{B}|A) = 1 - P(B|A) P(B−C∣A)=P(B∣A)−P(BC∣A)P(B-C|A) = P(B|A)-P(BC|A) P(AB)=P(A)P(B∣A)P(AB)=P(A)P(B|A) ⋃i=1nAi=Ω,AiAj=Φ,B=⋃i=1nAiB,P(B)=∑i=1nP(A)P(B∣A)\bigcup_{i=1}^n A_i = \Omega, A_iA_j = \Phi, B=\bigcup_{i=1}^n A_iB, P(B) = \sum^n_{i=1}P(A)P(B|A) ⋃i=1nAi=Ω,AiAj=Φ,P(Aj∣B)=P(Aj)P(B∣Aj)∑i=inP(Ai)P(B∣Ai)\bigcup_{i=1}^n A_i = \Omega, A_iA_j = \Phi, P(A_j|B)=\frac{P(A_j)P(B|A_j)}{\sum^n_{i=i}P(A_i)P(B|A_i)} P(ABˉ)=P(Aˉ∪Bˉ)P(\bar{AB})=P(\bar{A} \cup \bar{B})