俄罗斯轮盘：该不该再旋转？

Russian roulette

专题: Probability / 概率
难度: L4
来源: QuantQuestion

题目详情

I have a revolver which holds up to six bullets. There are two bullets in the gun, in adjacent chambers.I am going to play Russian roulette (on my own!),I spin the barrel so that I don't know where the bullets are and then pull the trigger. Assuming that I don't shoot myself with this first attempt, am I now better off pulling the trigger a second time without spinning or spin the barrel first?

解析

不旋转更安全。

设 6 个弹膛中有 2 发子弹且相邻，旋转后第一次扣扳机未中弹，说明当前弹膛是 4 个空弹膛之一。

在这 4 个空弹膛中，只有“紧挨着子弹对之前的那个空弹膛”会导致下一次（不旋转、转到下一个弹膛）中弹，因此

\mathbb{P}(\text{下一次中弹}\mid\text{本次未中弹且不旋转})=\frac{1}{4}.

若再旋转，下一次中弹概率回到先验 $2/6=1/3$ 。

因为 $1/4<1/3$ ，所以 $\boxed{不旋转更好}$ 。