The addition rule finds the probability that at least one of two events occurs. This rule appears in probability tables, card problems, survey data, and event planning whenever overlap matters.
Definition
The addition rule finds the probability that at least one of two events occurs. It adds the probabilities of the two events and then subtracts any overlap so the shared outcomes are not counted twice.
💡 Intuition
If you want “A or B,” start by adding A and B. Then fix the double-counting by removing the part that belongs to both events.
🎯 Core Idea
“Or” usually means union, not simple addition. Overlap changes the answer.
Example
Formula
Notation
A \cup B means “A or B,” including the case where both happen.
🌟 Why It Matters
This rule appears in probability tables, card problems, survey data, and event planning whenever overlap matters.
💭 Hint When Stuck
Before you calculate, ask whether the two events can happen together. If yes, you probably need the subtraction term.
Formal View
Related Concepts
🚧 Common Stuck Point
Students often add two probabilities and stop, forgetting that the overlap has been counted twice.
⚠️ Common Mistakes
- Adding probabilities without subtracting overlap
- Using the addition rule for “and” problems
- Assuming the overlap is zero without checking the context
Go Deeper
Frequently Asked Questions
What is Addition Rule in Statistics?
The addition rule finds the probability that at least one of two events occurs. It adds the probabilities of the two events and then subtracts any overlap so the shared outcomes are not counted twice.
What is the Addition Rule formula?
When do you use Addition Rule?
Before you calculate, ask whether the two events can happen together. If yes, you probably need the subtraction term.
Prerequisites
Next Steps
How Addition Rule Connects to Other Ideas
To understand addition rule, you should first be comfortable with compound events and stat sample space. Once you have a solid grasp of addition rule, you can move on to conditional probability.