Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and 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 these game-show proxies for 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 simple 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.

中文翻译：

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蒙蒂·霍尔睡美人

受Monty Hall问题及其流行的简单解决方案的启发，我们提供了许多游戏节目拼图，类似于臭名昭著的Sleeping Beauty Problem（及其上的变化），但更容易解决。我们在游戏节目（如Monty Hall's）中将参赛者取代了《睡美人》的觉醒，并以增加Monty Hall问题中门的数量的方式增加觉醒/参赛者的数量，从而更容易了解解决问题的方法是。我们证明了这些关于“睡美人问题”及其变化形式的游戏秀代理可以通过贝叶斯定理的简单应用来解决。这意味着我们将以信任或信任程度来表述我们的分析。但是，我们还将根据相对频率重新分析。全面的，我们的论文旨在通过一个简单但不平凡的例子展示解决科学哲学问题的一种经过实践检验的策略的有效性，即为该问题开发一个简单的模型并更改其参数。鉴于“睡美人问题”比“蒙蒂·霍尔问题”更受挑战，因为他们对许多人初次遇到概率的直觉提出了挑战，因此，我们认为将这种策略应用于这个难题对我们而言在教学上很有用。