Complementary events are important in probability because they make calculations easier.

An event's complement includes all the possible outcomes that are not part of that event.

Let’s look at an example:

• If event A happens with a probability of 0.7, then the complement of A (which is not A) has a probability of 0.3. This is because you can find it by subtracting from 1. So, if P(A) is 0.7, then P(A') = 1 - P(A) = 0.3.

This idea is really useful. If you know the complement of an event, you can quickly find the probability of the event itself. This is especially handy when the event is complicated to calculate.

So, understanding complementary probabilities can really help you solve problems more efficiently!