Proving two events are independent given that one has a probability of 1

[LCBlazer07]

Show that an event A is independent of every event B if P(A)=0 or P(A)=1.


**I was able to prove the first part of this problem that is that the events are independent when P(A)=0. However I am stuck on the part where P(A)=1.


I have this so far:

P(A n B) = P(A)P(B/A)
= (1)P(B/A)
= P(B/A)

If the events are independent then P(A n B) = P(A)P(B) = (PB)

So basically i have to show P(B/A) = P(B)...but I do cannot find a way to do this.

 

[Office_Shredder]

Try it the other way:
P(A n B) = P(B)P(A/B)

 

[LCBlazer07]

Ok, so i started using that suggestion and got the following...

P( A n B) = P(B)P(A/B)
then I was going to say that P(A n B) = P(B), but I how can I prove that P(A/B)=1 without assuming that A and B are independent.

 

[LCBlazer07]

thanks for the suggestion, but I was able to solve this problem by using the complement.