sample space
Before you can talk about the chance of anything, you first have to list everything that could possibly happen. Roll one ordinary die and the things that can happen are: a 1, a 2, a 3, a 4, a 5, or a 6. That complete list of every possible result is the sample space. It is the stage on which all probability is acted out.
Formally the sample space, usually written with the Greek letter Omega (Ω), is the set of all distinct outcomes of an experiment, where exactly one of them must occur and no two can occur at once. For a single coin toss Ω = {heads, tails}. For the number of car accidents a driver has in a year it might be {0, 1, 2, 3, ...} stretching on forever. For the exact dollar amount of a fire-insurance claim it could be every real number from 0 upward, a continuous range rather than a tidy list.
Actuaries pin down the sample space first because it forces honesty about what is being modeled. If you forget that a claim could be zero (the policy is in force but nothing happens) or that it could be enormous (a total loss), your later probabilities will be wrong no matter how clever the arithmetic. The shape of the sample space — a short list, a never-ending count, or a continuous range — also decides which kind of distribution and which tools you may use.
For one year of a single auto policy, an actuary might define the sample space as the number of claims: {0, 1, 2, 3, ...}. Most of the probability sits on 0 (no claim), a little on 1, and a vanishing sliver on the high counts.
The sample space is just the menu of possible results; the probabilities come later.
The sample space lists what can happen, not how likely each thing is — assigning the likelihoods is a separate step done with the probability axioms.