Question about probabilities of independent events? Consider a fair coin toss. Let $H$ be the event that a heads was thrown. Let $T$ be the event a tail was thrown. Given $H$ and $T$ are disjoint are then independent?
I don't really know how to do this. My initial though was yes but then I though for independent events $P(A\cap B)=P(A)P(B)$ but $A\cap B$ can't really happen since there is only one toss. So I'm unsure?
Any help?

Basically, what you have said in your second paragraph is correct: $P(H\cap T)=0$, and $P(H)P(T)=\frac14$, these are not equal so the events are not independent.
A useful informal way to think about this: two events are independent when the occurrence or non-occurrence of either does not affect the probability of the other happening.  In this case, the events are certainly not independent since a head occurring makes the probability of tails zero.
