We have looked so far at finding a single probability. This time, we're going to look at exhaustive events.

**What are exhaustive events?**

Exhaustive events are two events that describe everything that * could* happen.

For example, If I throw a coin, getting a head and getting a tail are the only two things that could happen so they are exhaustive

If a roll a dice, getting a 2 and getting a 3 are not exhaustive as they don't describe everything that could happen

If I roll a dice, getting a 2 and not getting a 2 are exhaustive as they describe everything that could happen.

**Probabilities adding to 1.**

We know that if something is certain, it has a probability of 1.

We can use this fact to find the probability of finding the probability of something not happening.

**Example: Find the probability of rolling a dice and not getting a 2**

Let's look at the example from before with the dice.

The probability I get a 2 and the probability I don't get a 2 are exhaustive, this means one of them is certain to happen. This means we can say that...

P_{(getting a 2)} + P(_{not getting a 2) }= 1

If we rearrange this...

P(_{not getting a 2) }= 1 - P_{(getting a 2).}

This means that if we know the probability of something happening, we can find the probability of it not happening.

P(_{not getting a 2) }= 1 -_{ }1/6 = 5/6