How do we determine if two events are independent?

Two events are independent if the outcome of the second event is not affected by knowing the outcome of the first outcome.

Example: If you have a bag of marbles of 3 red, 4 yellow, and 2 green, and you grab a yellow marble out of the bag then replace it what is the probability of grabbing another yellow one. Since you replaced it the probability of the second is not affected by the first one.