Sleeping Beauty on Monty Hall

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a simple solution to the notorious Sleeping Beauty Problem. We replace the awakenings of Sleeping Beauty by contestants on a game show like Monty Hall’s and we increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to see what the solution to the problem is. We show that the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and- true strategy for addressing problems in philosophy of science, i.e., develop a model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful