The use of probability theory is widespread in our daily life (gambling, investments, etc.) as well as in scientific theories (genetics, statistical thermodynamics). In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics (the physical theory that describes matter on the atomic scale), which gives rise to a new probability theory: quantum probability theory.Many professors argue that the essence of quantum mechanics is negative probability, or imaginary probability, or interfering probabilities, or something like that.
On the other hand, experts in probability and statistics have found quantum probability to be useless for modeling anything but atomic particles.
However, you only need regular probability theory for quantum mechanics. This has been explained by Jaynes and the Bayesians. Probability is not a physical thing, and is not essential to the theory. It is needed for testing, but that is true of all scientific theories.
Wave can interfere. Probabilities do not.