I get really confused on how to decide whether or not 2 events are independent. I can do the homework as long as I understand how to set it up, but that's where I get confused. How do I know whether or not an event is independent?
Generally a problem will tell you whether or not two events are independent, or you have to ascertain, from the description of the experiment whether or not an event is independent.
For example, if the experiment was determining the probability of getting a heads on a first flip of a coin, and a tails on the second flip of a coin - the two flips themselves are independent, as the probability of the first flips outcome does not affect the probability of the second flips outcome.
However, if somehow, say by magic, there was a way that the results of the first flip altered the probability of the second flip, then the second flip would be dependent on the first flip. Thats a cheesy example, but you get the idea. Generally, you should be able to look at the experiment that is being described and determine whether or not independence is occurring here or not.