Question

设ABC三个事件相互独立 试证A∪B与C相互独立

Answer 1

P[(A+B)*C]

= P(AC + BC)

= P(AC) + P(BC) - P(AC*BC) = P(AC) + P(BC) - P(ABC)

= P(A)*P(C) + P(B)*P(C) - P(A)*P(B)*P(C)

= [P(A) + P(B) - P(AB)]*P(C)

= P(A+B)*P(C)

证毕