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 · Accepted Answer

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       1    2        (    =          50      100        )   and the probability that   B occurs is       1    5        (    =          20      100        )  . 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                              70          100                                    =                  50          100                +                  20          100                                                  =                  probability that                       A                     occurs                +                  probability that                       B                     occurs.

Tyler Velasquez · Accepted Answer

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  #(black or ball)  =  #black  +  #balls  .

I know that there is the addition rule of probability,

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