Identify Exhaustive Events

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.