The Addition Rule is a helpful tool in probability. It's especially useful when we deal with mutually exclusive events.

But what does "mutually exclusive" really mean?

Simply put, it refers to events that can't happen at the same time.

For example, when you toss a coin, it can land on heads or tails, but not both at once.

Understanding the Addition Rule

The Addition Rule tells us how to find the chance of either of two mutually exclusive events happening.

To do this, we just add their individual chances together.

We can write this in a simple way:

$$P(A \cup B) = P(A) + P(B)$$

Here's what that means:

• $P(A \cup B)$ is the chance that either event $A$ or event $B$ happens.
• $P(A)$ is the chance of event $A$ happening.
• $P(B)$ is the chance of event $B$ happening.

Example Time!

Let’s look at an example with a six-sided die.

The chance of rolling a 2, $P(2)$, is $\frac{1}{6}$.

The chance of rolling a 3, $P(3)$, is also $\frac{1}{6}$.

Since you can’t roll a 2 and a 3 at the same time, we can use the Addition Rule:

$$P(2 \cup 3) = P(2) + P(3) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$$

Wrapping It Up

The Addition Rule makes figuring out probabilities for mutually exclusive events much easier.

It helps us understand and analyze different situations in probability better.

So, the next time you have to think about such events, keep this handy rule in mind!