Proof : An event is independent from every other event iff its probability is 0 or 1 As said in the title I need to prove that an event is independent from all other events iff its 0 or 1. One side is pretty simple, if I assume the event is 0 or 1 probability the answer is immediate.
I'm having trouble formulating the other side, i.e if I assume there is an event which is independent from all other, I need to show its probability is 0 or 1. I understand that if I assume such an event exists its occurrence will never affect the probability of every other event, therefore if I assume by contradiction that its probability is not 0 or 1, 
an observer cannot be sure that such an event is independent from all others, because he will not be sure of when it will happen or not.
Frankly what I wrote doesn't sound exactly right to me, but I can't seem to formulate any mathematical proof, I'm not sure of how to represent the fact its independent from all the other events mathematically.
Hopefully you could give me a hint on where to start at least, thanks!

I'll retract this as an answer but leave it here for those similarly confused
Not true it seems to me.
Consider the probablity of getting heads or tails (H, T) on the toss of a coin and also getting a number (1 to 6) on the throw of a dice. p(H) = 1/2 and p(2) = 1/6. But the events are surely indenpendent ?
From the subsequent answer and comments I assume that I should be considering $\Omega $ as a probability space consisting of the combined events. So (H, 2) is not independent from all the other outcomes - correct ?
