Understanding complementary events is really important when working with probability. It helps make solving problems easier.

So, what are complementary events?

They are outcomes that are opposites.

For example, if we say event A is "it rains tomorrow," then the opposite event, called A', is "it does not rain tomorrow."

Here’s a key point to remember:

• The total probability of complementary events is always 1.

This means:

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

In simple terms, if you know the chance of one event happening, you can easily find the chance of the other event.

Let’s say the chance of it raining tomorrow, or P(A), is 0.7.

You can find the chance of it not raining, or P(A'), by doing this calculation:

1 - 0.7 = 0.3.

Using complementary events makes calculations easier, especially when we deal with phrases like "at least one" or "none."

This approach makes it less confusing and more straightforward for students learning about probability in their AS-Level mathematics classes.