In quantum mechanics, probabilities are typically understood as measures of the likelihood of different outcomes occurring in a given experiment. However, the interpretation of probabilities in quantum mechanics is a subject of philosophical debate and various interpretations exist.
One interpretation is the frequentist interpretation, which aligns with your description of probabilities as the asymptotic frequency of events as the number of independent trials tends to infinity. According to this view, probabilities represent objective frequencies of outcomes in repeated experiments. However, this interpretation encounters challenges in the context of quantum mechanics, where certain events do not have well-defined frequencies and can exhibit probabilistic behavior even in single instances.
Another interpretation is the Bayesian or subjective interpretation, which considers probabilities as measures of personal belief or confidence. According to this perspective, probabilities reflect an individual's degree of knowledge or subjective assessment of the likelihood of different outcomes. Bayesian probabilities can be updated based on new information and incorporate prior beliefs and evidence.
It's worth noting that the interpretation of probabilities in quantum mechanics is an area of ongoing discussion and philosophical inquiry. Different physicists may have different views on the nature of probabilities in this context. Ultimately, the choice of interpretation may depend on one's philosophical stance, personal inclinations, or practical considerations when applying quantum mechanics to specific scenarios.