When we talk about probability, it's really important to know what a complement is!

So, what is a complement? It’s just a way of describing all the outcomes that don’t belong to a certain event.

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

If the event we’re talking about is rolling an even number (like 2, 4, or 6), then the complement is rolling an odd number (which would be 1, 3, or 5).

Now, how do we figure out the probability of the complement? Here’s a simple guide:

1. Find the probability of the event: For our example, if we want to know the chance of rolling an even number (let’s call this event A), we find that there are three even numbers out of six possible outcomes. So, the probability of event A is $P(A) = \frac{3}{6} = \frac{1}{2}$.

2. Use the complement rule: To find the probability of the complement of event A (we can call this $P(A')$), we use this formula:

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

   In our example, that means:

   $P(A') = 1 - P(A) = 1 - \frac{1}{2} = \frac{1}{2}$

3. Check your work: It’s good to double-check! The probabilities of an event and its complement should add up to 1. In this case:

   $P(A) + P(A') = \frac{1}{2} + \frac{1}{2} = 1$

Let’s sum it all up in a quick list!

• Identify the event: Figure out the probability of what you’re looking at.
• Calculate the probability of the complement: Use the complement rule.
• Verify: Make sure the probabilities add to 1.

Knowing about complements can really help you tackle many probability problems with ease!