The way I came up with my attempt was just to notice that when you are looking at the probability of two independent events happening together, you multiply the

The way I came up with my attempt was just to notice that when you are looking at the probability of two independent events happening together, you multiply them; and if you want the probability of A or B or both, you add them and then subtract the probability of (A and B). I guess the reason the multiplication rule doesn’t work for (A && A) is that those two variables are clearly not independent, since they’re the same variable.