⭐ General Addition Rule

The general addition rule tells you how to find the probability that A or B happens — even when the events overlap.

📌 The formula

Why subtract the intersection?
Because if A and B can happen together, that overlap gets counted twice when you add and . The rule fixes that by removing the double-counted part.

🧠 When do you use it?

Always use the general rule unless you know the events are mutually exclusive.

• If the events cannot happen together (mutually exclusive), then
  
  and the rule simplifies to
  

🎯 Quick Example

Suppose you roll a die.
Let

• “roll an odd number”
• “roll a number ≤ 3”

These events overlap (1 and 3 are in both).
Using the general rule:

🧩 Intuition

Think of two circles in a Venn diagram.

• Add the size of circle A
• Add the size of circle B
• Subtract the part where they overlap so you don’t count it twice

That’s the whole idea.