I know that third axiom says that $P(A) + P(B)$ can work if those two sets are disjoint.
What I cannot understand is how this: https://wikimedia.org/api/rest_v1/media/math/render/svg/47f22fe03df467b1d20785e5026bac39fabd9edc
Is telling me that. I know it can be bothersome but could someone explain me step-by-step how to read and solve questions like: "What does the $U$ and $E_i$ mean?" That would be really helpful.
Thank you!
In the image there is a set $E$ composed of possibly infinite events $E_i$. So the set looks like this: $ E = \{E_1, E_2, ..., E_i, ...\}. $ With $i$ being any subscript $0<i<\infty$.
Each individual $E_i$ is comparable to the $A $ and $B$ you gave in your example.
Now the expression is saying if you take the union (that is what $\bigcup$ means) of any number of your disjoint events $E_i$, and then find the probability of an event in that new set occuring, it will be equal to the summation of the probabilities of the individual events $E_i$ in your new set.