Calculating the chance of opposite events can be tricky, especially for beginners in probability.

So, what are complementary events?

They are two outcomes from one experiment where only one can happen at a time, and together they cover all possible results.

Let’s break it down with a simple example:

Imagine you’re rolling a die.

If you want to know the chance of rolling a 3, we say the chance is $P(A) = \frac{1}{6}$. This means there is one way to roll a 3 out of six possible numbers.

Now, what about the opposite event?

That’s where $P(A')$ comes in.

You can find its probability using this easy formula:

$$P(A') = 1 - P(A)$$

This means that the total chance of all outcomes adds up to 1.

However, before you can figure out the opposite event, you first have to know the chance of your original event.

Here are some simple steps to help you:

1. Figure out the original event $A$ and its probability $P(A)$.
2. Use the formula $P(A') = 1 - P(A)$ to find the opposite event’s chance.

With some practice and a good grip on the basic ideas of probability, you can definitely get the hang of this.

Remember, the first step might feel tough, but it’s super important for building your skills and confidence in probability!