The Addition Rule in probability helps us figure out how likely it is for at least one of a few events to happen. Let's look at some examples to make this clearer:

1. Mutually Exclusive Events: Picture a bag filled with only red and blue marbles. If you want to know the chance of picking either a red marble ($P(R)$) or a blue marble ($P(B)$), you can just add their chances together: $P(R \text{ or } B) = P(R) + P(B)$

2. Non-Mutually Exclusive Events: Now, imagine you have two dice. You want to find the chance of rolling a three ($P(3)$) or rolling an even number ($P(E)$). In this situation, these events overlap because rolling a three doesn't change anything about the even numbers: $P(3 \text{ or } E) = P(3) + P(E) - P(3 \text{ and } E)$

These examples show that the Addition Rule makes it easier to do our probability calculations!