Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose a simple formal language with arrow notation ($\gets$) for sampling from a distribution and with observe statements for conditioning (updating, belief revision). We demonstrate the usefulness of this simple language by solving several famous puzzles from probabilistic decision theory. The operational semantics of our language is expressed via the (finite, discrete) subdistribution monad. Our broader message is that proper formalisation dispels confusion.

翻译：概率谜题常常令人困惑，部分原因在于它们以充满模糊性与歧义的自然语言表述，部分原因在于缺乏一种被广泛接受且直观的形式化语言来表达它们。我们提出一种简单的形式化语言，该语言采用箭头符号（$\gets$）表示从分布中采样，并使用观察语句进行条件化（更新、信念修正）。通过解决概率决策理论中的多个著名谜题，我们展示了这种简单语言的实用性。该语言的操作语义通过（有限、离散）子分布单子来表达。我们更广泛的观点是：恰当的形式化能够消除困惑。