Calculating the chances of different events happening is pretty simple once you understand it. Let’s go through it step by step!

What are Independent Events?

First, let's talk about independent events. These are events that don’t impact each other.

For example, when you flip a coin and roll a die, the coin flip (heads or tails) doesn’t change what number you get on the die (from 1 to 6).

The Multiplication Rule

To find out the chance of both events happening, you use the multiplication rule. This means you multiply the chances of each independent event.

Here’s a simple way to think about it:

• If the chance of flipping heads ($P(H)$) on a coin is $0.5$, that means there’s a 50% chance.
• The chance of rolling a 4 ($P(4)$) on a six-sided die is $1/6$, which is about $0.167$.

So, to find the chance of flipping heads and rolling a 4 at the same time, you would calculate:

$$P(H \text{ and } 4) = P(H) \times P(4) = 0.5 \times \frac{1}{6} = \frac{0.5}{6} \approx 0.0833$$

This means there’s roughly an 8.33% chance of both happening!

What If There Are More Events?

If you want to find the chance of more than two events, just keep multiplying! For example, if you also want to consider rolling a 5 on the die, you would include that as well:

$$P(H \text{ and } 4 \text{ and } 5) = P(H) \times P(4) \times P(5)$$

Since $P(5)$ is also $1/6$, it would look like this:

$$P(H \text{ and } 4 \text{ and } 5) = 0.5 \times \frac{1}{6} \times \frac{1}{6} = \frac{0.5}{36} \approx 0.0139$$

In Conclusion

So, remember: if the events don’t affect each other, just multiply their chances together! It’s an easy trick that makes figuring out probabilities more fun and manageable.