Of the different notions of probability discussed in philosophy,
objective notions seem to be more naturally applicable to physics. In
classical physics, probability enters primarily in the reduction of
thermodynamical phenomena (e.g., the free expansion of a gas) to
statistical regularities of the underlying particle mechanics. For
this purpose, a notion of probability that is based on time averages
given suitable properties of the dynamics, is particular suited.
This leads to a special version of a frequentist interpretation.
Quantum mechanics seems, at first, to require a very different notion
of probability. On the other hand, the pilot-wave model by de Broglie
and Bohm is also deterministic and can be understood in analogy to
classical statistical mechanics. Thus, this statistical notion of
probability is capable of dealing in a unified way with both classical
and quantum physics.