in the last section we learned how to calculate and probabilities even when all the outcomes aren't equally likely using the multiplication rule in this section we are going to derive a similar rule for or probabilities so let's first remember what that operator or does when stuck in between two different events okay so here I have a little Venn diagram of two events A and B in a sample space now if I look at a or b that means I want all the outcomes in a either in a or in b so everything in a I want that I want everything in b and I want everything that's in both okay that is pictorially what the new event A or B is and now I want to find the probability of A or B so to think about this this geometric understanding is going to be very helpful okay so A or B is everything in a together with everything in B right so let's just separate them and see what happens so let's start by taking everything in a okay just in a and now let's add in everything in b something like that okay now that gets pretty close right it gets everything in a that gets everything in B so if we just add these probabilities together we get pretty close but there's a problem we end up double counting a region this region right here in between we count once when we count the probability of a again when we account for the probability of B so if we just add probability of a with probability of B we are counting this region twice now we do want to count it but we only want to count it once so what I need to do is I need to correct that over counting so to do that because I'm counting it twice I'm going to subtract that region once okay now remember this region here is the region A and B that's all the outcomes that are common to A and B so I'm going to subtract the probability of the outcomes they have in common because again I count them twice I do want to count them but only once so I subtract one of them away this gives our addition rule that probability of any two events A or B is equal to the probability of a plus the probability of B minus the probability of a and B