Question

已知P(A)=P(B)=P(C)=0.25,P(AB)=0 P(AC)=P(BC)=1/6,求事件A B C 完全不发生

Answer 1

① P(ABC均不发生)=1-P(A∪B∪C)=1-P(A)-P(B)-P(C)+P(AB)+P(BC)+P(AC)-P(ABC)=1-0.25*3+0+1/6+1/6-0=7/12

②P(ABC至少发生一个）=P(A∪B∪C)=P(A)+P(B)+P(C)-P(AB)-P(BC)-P(AC)+P(ABC)=0.25*3-0-0-1/8+0=5/8