Question

互斥与独立事件的概率已知A,B为相互独立事件,B,C为互斥事件,P(A)=0.55,P(B)=0.35,P(C)=0.1

Answer 1

P(AUBUC)=P(A)+P(B)+P(C)-P(A and B)-P(A and C)-P(C and B)+P(A and B and C)

其中P(A and B and C)=0=P(B and C) 因为B和C不能一起发生

P(A and B)=P(A)*P(B)=0.1925 因为A,B为相互独立事件

最后,带入数据

P(AUBUC)=0.55+0.35+0.15-0.12-0.1925=0.7375