设随机事件A B C相互独立 且P(A)=0.4 P(B)=0.5=P(C).求P(A-C|ABUC)=?
问题描述:
设随机事件A B C相互独立 且P(A)=0.4 P(B)=0.5=P(C).求P(A-C|ABUC)=?
答
用C'表示C的对立事件,则
A-C=AC',
(A-C)(AB∪C)=AC'(AB∪C)=ABC',
A,B,C相互独立,
∴P(ABC')=P(A)P(B)[1-P(C)]=0.4*0.5*(1-0.5)=0.1,
P(AB∪C)=P(AB)+P(C)-P(ABC)=0.2+0.5-0.1=0.6,
∴P(A-C|AB∪C)=P[(A-C)(AB∪C)]/P(AB∪C)=1/6.