③ P (BC )=P (B )P (C )
④ P (ABC )=P (A )P (B )P (C )
则称A ,B ,C 这三个随机事件相互独立.
好,回顾了三个随机事件相互独立的定义后,现在我们来正式做这道题.
首先,题中说A 与B 相互独立,所以有 P (AB )=P (A )P (B ).
由于0≤P (AC )≤P (C ),而P (C )=0,所以0≤P (AC )≤0,所以P (AC )=0;又因为P (C )=0,所以无论P (A )是什么数,都有P (A )P (C )=0;由于P (AC )=0,P (A )P (C )=0,所以有 P (AC )=P (A )P (C ).
由于0≤P (BC