# I know that there is the addition rule of probability,

I know that there is the addition rule of probability, but I want to understand the intuition behind it. Specifically, why does OR signifies addition in probability theory?
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Brianna Sims
I suppose that you question is this:

If two events $A$ or $B$ cannot occur simultaneously, then why is the probability that $A$ occurs or $B$ occurs equal to the probability that $A$ occurs plus the probability that $B$ occurs?

Suppose that there are, say, 100 possibilities, that $A$ takes place in 50 of them and that $B$ takes place in 20 of them. Then the probability that $A$ occurs is $\frac{1}{2}\left(=\frac{50}{100}\right)$ and the probability that $B$ occurs is $\frac{1}{5}\left(=\frac{20}{100}\right)$. What is the probability that $A$ occurs or $B$ occurs? Well, out of those 100 possibilities, $A$ occurs or $B$ occurs exactly in 70 of them (this is where I use the fact that $A$ or $B$ cannot occur simultaneously). So, the probability that $A$ occurs or $B$ occurs is
###### Not exactly what you’re looking for?
Tyler Velasquez
Because the probability is the number of favorable draws over the total number of draws.
And the number of favorable draws are additive: the number of [red or green] balls is the number of red plus the number of green.

Caution:
The additive rule is only valid for disjoint categories. For example, if you have black/white balls and dice, it is not necessarily true that
$\text{#(black or ball)}=\text{#black}+\text{#balls}.$