Quantum mechanics is typically considered a probabilistic theory rather than a deterministic one. It provides a mathematical framework that allows for predicting the probabilities of various outcomes when measuring physical properties of quantum systems. However, it does not generally provide deterministic predictions for the exact outcomes of individual measurements.
The probabilistic nature of quantum mechanics is encapsulated in the concept of the wavefunction, which describes the state of a quantum system. The wavefunction contains information about the probabilities of different measurement outcomes, and when a measurement is made, the system "collapses" into one of the possible states according to these probabilities.
This probabilistic behavior is often illustrated by the famous thought experiment known as Schrödinger's cat. In this scenario, a cat inside a sealed box is in a superposition of being both alive and dead until the box is opened and the cat is observed. At that point, the wavefunction collapses, and the cat is found to be either alive or dead with a certain probability.
However, it's worth noting that there are deterministic aspects within the theory. The time evolution of the wavefunction is described by the Schrödinger equation, which is a deterministic equation. It governs how the wavefunction evolves over time in the absence of measurement or interaction with other systems. Nevertheless, when it comes to actual measurement outcomes, quantum mechanics provides probabilities rather than determinism.
The probabilistic nature of quantum mechanics has been extensively tested and confirmed by experiments, including the famous Bell's theorem experiments, which ruled out local hidden variable theories that would allow for deterministic predictions.