random experiment
A random experiment is any action or process whose outcome you cannot predict for sure ahead of time, even though you can describe in advance all the things that might happen. Tossing a coin, rolling a die, drawing a card, measuring how long until a bus arrives, or checking whether it rains tomorrow are all random experiments. The defining feature is not that the world is mysterious, but simply that before you do it you genuinely do not know which of several possible results will occur.
Two ingredients make something a random experiment in the precise sense probability uses. First, the experiment must be repeatable in principle, or at least imaginable as one trial among many under the same conditions. Second, you must be able to list, before running it, the complete collection of conceivable results — for a coin that is heads and tails, for a die it is the faces 1 through 6. You do not need to know which result you will get; you only need to know the menu of possibilities. That menu is what the next idea, the sample space, names.
It is worth being honest about what randomness means here. A flipped coin obeys ordinary physics, so in a sense its result is determined by how it was thrown; we call it random because we cannot or do not track all those details, so from our point of view the outcome is unpredictable. Probability theory does not require true cosmic randomness — it only requires our genuine uncertainty about which listed outcome will appear. This is the starting point on which the whole subject is built.
Rolling a single fair die is a random experiment: before the roll you can write down the full list of possible results — 1, 2, 3, 4, 5, 6 — but you cannot say which one will land face up.
Known menu of outcomes, unknown which one — that combination is exactly a random experiment.
Random here means unpredictable to us, not necessarily uncaused; even a perfectly deterministic process counts if we cannot foresee its specific result.