Resolving the Sleeping Beauty Paradox: A Mathematical Analysis of Subjective and Objective Probabilities

The Sleeping Beauty paradox challenges traditional interpretations of probability by presenting a scenario where subjective experience and objective probability seem to diverge. In this work, we argue that the paradox arises from an ambiguous formulation of the problem, particularly regarding the information available to the subject and the overlap of events. By analyzing the essential elements of probability theory and examining the role of information and memory in the paradox, we provide a rigorous mathematical demonstration that shows that conflicting solutions derive from overlapping events and partial knowledge. Our analysis suggests that a clear and unambiguous formulation resolves the paradox, aligning subjective probabilities with objective reality.