Complementary events are really important when we talk about probability.

They make it easier to do calculations.

When we talk about an event, we use the letter $A$ to represent it.

The chance of event $A$ happening is called $P(A)$.

There’s also the opposite of event $A$, which we call $A'$.

We can find the chance of $A'$ by using this formula:

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

This means that the chances of $A$ happening and not happening always add up to 1.

Here’s an example:

• If $P(A) = 0.7$, that means there is a 70% chance that event A will happen.

• So, to find $P(A')$, we do the math: $1 - 0.7 = 0.3$.

This means there is a 30% chance that event A will not happen.

By understanding complementary events, we can solve problems more easily.

This is especially helpful when figuring out $P(A)$ is too hard to do directly.