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俄罗斯轮盘 III

Russian Roulette III

专题
Finance / 金融
难度
L2

题目详情

6 膛左轮里随机放入 2 发子弹（位置随机）。开始时转动弹巢一次并固定。

朋友先手扣扳机且存活。轮到你时，你可以选择：

  • 不重转，直接扣扳机（沿用当前弹巢状态）；
  • 或重转弹巢再扣扳机。

问：选择“重转”与“不重转”的生存概率相差多少？（重转生存概率减去不重转生存概率）

You are engaged in a game of Russian Roulette with a companion. The revolver, which has 66 chambers, is loaded with 22 bullets placed at random. To start, the cylinder is spun to randomize the arrangement of the chambers. You and your friend take turns pulling the trigger until one of you fires the loaded chamber and loses. Your friend takes the first turn and survives the initial trigger pull. You now have the option to either spin the barrel again or keep it as is before taking your shot. What is the difference in the probability of your survival between spinning the barrel and not spinning it?

解析

朋友已空枪一次，说明当前击发膛是空的。

  • 若不重转：剩余 5 个膛里有 2 发子弹，因此你生存概率为 3/53/5。
  • 若重转：6 个膛里有 2 发子弹，生存概率为 4/6=2/34/6=2/3。

差值为

23−35=115.\frac{2}{3}-\frac{3}{5}=\frac{1}{15}.

Original Explanation

If you decide not to spin the barrel, the likelihood of your survival is 35\frac{3}{5}, as one of the safe chambers has already been activated by your friend. On the other hand, if you choose to spin the barrel, the probability of surviving becomes 46\frac{4}{6}, since any of the 6 chambers can be in play, 2 of which are fatal. Therefore, the difference in probabilities is:

46−35=115\frac{4}{6} - \frac{3}{5} = \frac{1}{15}