In quantum mechanics, probabilities are assigned to events based on the mathematical formalism known as wave functions. The wave function describes the state of a quantum system and provides information about the probabilities of different outcomes when measurements are performed on the system. However, it's important to note that the assignment of probabilities in quantum mechanics is different from classical probability.
In classical probability, probabilities are assigned based on the relative frequencies of events observed in a large number of trials. However, in quantum mechanics, probabilities are associated with the outcomes of measurements, and these outcomes are inherently probabilistic.
One of the key features of quantum mechanics is the principle of superposition, which allows quantum systems to exist in a combination of multiple states simultaneously. When a measurement is made on a quantum system, the wave function "collapses" to one of the possible outcomes, and the probabilities of different outcomes are given by the squared magnitudes of the corresponding amplitudes in the wave function.
The fact that non-zero probabilities are assigned to events that have never been observed is a consequence of the superposition principle and the probabilistic nature of quantum measurements. In quantum mechanics, all possible outcomes are considered and accounted for in the mathematical formalism, even if they have not been observed in previous experiments.
It's important to note that the assignment of probabilities to unobserved events does not imply that these events will necessarily occur when a measurement is made. Rather, the probabilities describe the likelihood of obtaining a particular outcome when a measurement is performed on a quantum system in a specific state.
The probabilistic nature of quantum mechanics has been extensively verified through a wide range of experiments, and the predictions of quantum mechanics have been found to be in excellent agreement with observational data.