What is the Independence Probability Theory?
Two events are independent if their joint probability is equal to the product of their probabilities. More simply, two events are independent if the outcome of one event doesn't affect the probability of the other event.
Imagine you're drawing cards from a deck. Consider the probability that the first card you draw is red, and the probability that the second card you draw is red. If you don't replace the first card after you draw it, then the two probabilities are dependent -- the probability that the second card is red depends on whether the first card was red or not. Conversely, if you do replace the first card after you draw it and then shuffle, then the two probabilities are independent -- it doesn't matter what you drew the first time, you're drawing from the full deck the second time.
It's important to keep track of which events are independent and which events are dependent, because the probability math changes based on that distinction. If probabilities are independent, then you can just multiply them together -- the probability of rolling a 2 on a d6 is ⅙, the probability of rolling two 2's on 2d6 is ⅙ * ⅙ = 1/36, etc. But if the probabilities are dependent, then the math is much more complicated.