Kolmogorov's axioms specify a set of elementary events $E$ which is the sample space in modern theory. He then specifies a field of probability which is the power set of $E$. The axioms state $P(E) = 1$ and to construct a field of probability all the elementary events of $E$ are assigned probabilities.
My question is why does some of the modern literature and problems exclude specification of the elementary events and probability for each elementary event? There is also no specification of the sample space.
For instance, I'm reading the following problem and keep asking myself: "What is the sample space?" "What are the elementary events and their probabilities?". Is this information not required? Thanks