The Addition Rule: A Simple Guide to Probability

The Addition Rule is really important when we're looking at the chances of different events happening together, especially when there are two or more events. Let's break it down simply:

1. What Are Events?
   In probability, events can either happen at the same time or be separate. For example, if you roll a die, getting a 2 or a 3 is separate. You can't roll a 2 and a 3 at the same time.

2. Basics of the Addition Rule:
   The Addition Rule says that if events A and B are separate (or mutually exclusive), you can find the chance of either event happening by just adding their probabilities together. This looks like this:
   $P(A \cup B) = P(A) + P(B)$
   So, you simply add their chances!

3. When Events Overlap:
   Sometimes, events can happen at the same time. In this case, you have to take away the chance of them happening together so you don’t count it twice. The formula for this looks like:
   $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

4. Why This Is Important:
   Using the Addition Rule helps us find the right chance of one event or the other happening. This is super helpful in real life, like when you’re playing games, watching sports, or even making choices.

5. How to Use It in Real Life:
   Think about planning a game. Knowing how likely you are to win or lose helps you make better choices. The Addition Rule gives you clear information, making it a really important tool when we talk about chances!