# Introducing the Addition Rule¶

Let's use again the example of flipping a coin and then throwing a dice. But now imagine we want to know the probability of getting Heads and $5$ or getting Tails and $2$.

Again, in a small example like this one we can solve it as before:

If $E=\{H5,T2\}$ then $P(E)=\dfrac{|E|}{|\Omega|}=\dfrac{2}{12}=\dfrac{1}{6}$, because it has equally likely results and $\Omega=\{H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6\}$.

But let's think about it in terms of our tree diagram:

If we look closely, we are interested in two different branches, each of which has a probability of $\dfrac{1}{12}$.

So to calculate the probability of getting either of them, we can add the two probabilities: $P(H5 \ or \ T2)=P(H5)+P(T2)=\dfrac{1}{12}+\dfrac{1}{12}=\dfrac{2}{12}=\dfrac{1}{6}$.

In general, when we have two (or more) outcomes/events and we want the probability of *either of them happening*, we are going to add the individual probabilities.

Of course, this is going to be called the **Addition Rule**.

In terms of the tree diagram, we can say that the probability down the branches is the addition of the probabilities.

Again, one final and important remark: The Addition Rule has certain conditions that need to be met in order to use it, but we are going to dig deeper into that in future videos.