A Bayesian Solution to the Sleeping Beauty Problem Aided by Exemplification from the Solution of the Bertrand's Box Problem and Elimination of the Confusion and Discrepancy Therein

Pitamber Kaushik

Abstract: The paper discusses and aims to prove that the thirder position with respect to the Sleeping Beauty Problem is the correct one, i. e. the probability asked in the problem is 1/3. Bayesian Analysis and an analogical correspondence drawn with the solved but similar Bertrands Box Problem constitute the twofold approach, employed to address the problem. The two methods, one objective and one subjective, both conclude by meticulous and unambiguous arguments and definitions, that the probability is indeed 1/3, also stressing how seemingly inconspicuous observations, alter the priori probabilities of an experiment and disrupt the original partitioning of events.

Keywords: Sleeping Beauty Problem, Bayesian Probability, Partitioning of Sample Space, Priori Probabilities, Bertrands Box Problem