Randomness refers to a situation where repeating the same conditions that produce a possible outcome can result in a different outcome, where the only noticeable, perceivable, or measurable distinction between repetitions is time itself.

True, or absolute, randomness implies that there is no distinction between repetitions except for time. Approximate randomness implies there is no perceivable or noticeable difference - though there could be.

Because knowing whether a situation is absolutely random requires measurement, and an appromixately random situation is one in which there is no real measurable distinction, it is impossible to know whether a situation is absolutely random. Said another way, it is always possible to wrongly assume one is dealing with an absolutely random situation.

Likelihood refers to the number of times a specific outcome would occur in a scenario where the random situation is repeated indefinitely, given the number of possible outcomes that could occur from that scenario.

Probability is a method for calculating likelihood that assumes absolute randomness.

Because it is impossible to know whether a situation is absolutely random, there is always a possibility that a probability will be wrong. Not simply that the prediction is wrong, but that its application is inappropriate.