Understanding how to use the addition and multiplication rules in probability can be much easier when we look at real-life examples.

Addition Rule

The addition rule helps us find the chance of one event happening or another.

A simple example is rolling a die.

Let’s say you want to find the chance of rolling either a 3 or a 5.

You can add up the chances of each one:

• The chance of rolling a 3: ( P(3) = \frac{1}{6} )
• The chance of rolling a 5: ( P(5) = \frac{1}{6} )

Now, using the addition rule, you can calculate:
[ P(3 \text{ or } 5) = P(3) + P(5) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} ]

So, there’s a 1 in 3 chance you will roll either a 3 or a 5.

Multiplication Rule

The multiplication rule is about finding the chance of two independent events happening together.

Let’s think about drawing cards from a deck.

What’s the chance of drawing a heart first and then drawing another heart right after?

1. The chance of drawing a heart first:
   ( P(\text{Heart 1}) = \frac{13}{52} )

2. The chance of drawing a heart second (after one heart has been drawn):
   ( P(\text{Heart 2} | \text{Heart 1}) = \frac{12}{51} )

Now, using the multiplication rule:
[ P(\text{Heart 1 and Heart 2}) = P(\text{Heart 1}) \times P(\text{Heart 2} | \text{Heart 1}) = \frac{13}{52} \times \frac{12}{51} = \frac{1}{17} ]

So, the chance of drawing two hearts in a row is 1 in 17.

These examples help us understand the rules better and show us how to use them in real situations!