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