返回题库

俄罗斯轮盘：该不该再旋转

Russian roulette

专题
Probability / 概率
难度
L4

题目详情

概率题：俄罗斯轮盘：该不该再旋转？。

英文原题

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

P(下一次中弹∣本次未中弹且不旋转)=14.\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=1/32/6=1/3。

因为 1/4<1/31/4<1/3，所以 不旋转更好\boxed{不旋转更好}。

英文解析

This is a very typical, simple probability Brainteaser. It doesn't require any sophisticated or lateral thought. Just pure calculation.

Whenever you spin the barrel you clearly have a two in six, or one in three chance of landing on a chamber containing a bullet.

If you spin and pull the trigger on an empty chamber, what are the chances of the next chamber containing a bullet? You are equally likely to be at any one of the four empty chambers but only the last of these is adjacent to a chamber containing a bullet. So there is now a one in four chance of the next pull of the trigger being fatal. Conclusion is that you should not spin the barrel. After surviving two pulls of the trigger without spinning the barrel the odds become one in three again, and it doesn't matter whether you spin or not (at least it doesn't matter in a probabilistic sense). After surviving that 'shot' it becomes fifty- fifty and if you are successful four times in a row then the next shot will definitely be fatal.