Random event without probability



Sorry in advance for the strange question.

Random events and probabilities seem to be inextricably coupled. On a side we have the physical event ("tossing a head when flipping a coin") on the other the numerical value P(X) = 0.5. Is it possible to conceive a random event for which a probability value is not defined? I don't mean that the probability is zero, but rather that the physical event does not admit a probability value.


I'm not sure what you mean by the probability value not being defined. Do you mean not known? For example, in the case of objects such as coins and dice, we make an inference based on symmetry and near perfection (fairness) that each side of a coin has 1/2 probability of occurring, and that each side of a six-sided has 1/6 probability of occurring.

But suppose that there are rare cases in which a coin could land on edge. We would not know that probability without conducting a large number of trials. Is this what you mean by not defined?