In other activities, we have looked 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 something **not **happening.

**Example: **

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

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

The probability that I get a 2 and the probability that I **don't **get a 2 are exhaustive, this means that 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

Time for some questions now.