最近在複習貝氏定理(Bayes’ theorem),總是逃不過一個經典的問題叫做 Monty Hall Problem 又稱蒙特霍問題、山羊問題或三門問題,我們最常聽到設定就是: 假設你正在參加一個遊戲節目,你被要求在三扇門中選擇一扇:其中一扇後面有一輛車;其餘兩扇後面則是山羊。你選擇了一道門,假設是一號門,然後知道門後面有什麼的主持人,開啟了另一扇後面有山羊的門,假設是三號門。他然後問你:「你想選擇二號門嗎?」轉換你的選擇對你來說是一種優勢嗎? (from wiki: https://en.wikipedia.org/wiki/Monty_Hall_problem) 很多人直覺會想,我一開始就選擇了一號門,跟之後主持人開門有什麼關係?為什麼拿獎的機率會變? 注意!其實主持人開門的動作恰好透露了他對於門後是否有獎品的信息,舉個例子,如果二號門後面就是車子,那麼主持人就一定不會開二號門,而是改開三號門,相反的,如果三號門後面有車子,那主持人就不會開三號門,如果主持人知道一號門後面有車子,那麼主持人就會隨機開二號門或者三號門。 開始算機率之前我們先把事件定義清楚: 事件: H1 = 車子在一號門,...
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Boundary element method for the Dirichlet problem for Laplace’s equation on a disk(arXiv) Author : Misael M....
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