Wall Street job interview
Let’s play a game of Russian roulette. You are tied to your chair. Here’s a gun, a revolver. Here’s the barrel of the gun, six chambers, all empty. Now watch me as I put two bullets into the barrel, into two adjacent chambers. I close the barrel and spin it. I put a gun to your head and pull the trigger. Click. Lucky you! Now I’m going to pull the trigger one more time. Which would you prefer: that I spin the barrel first or that I just pull the trigger?
Solution
6个轮盘里面有两个相邻的子弹，第一枪没有子弹。现在问你第二次开枪时，我是否应该首先旋转一下？所以设两个事件：
\[A=\{\text{survive on the first try}\}.\\
B=\{\text{survive on the second try}\}.
\]
- 如果首先旋转：那么之前的结果就不影响了，所以便和第一次是等价的了。因此：
\[P(B|A)=P(A) = \frac{4}{6}=\frac{2}{3}
\]
- 如果不旋转，此时：
\[P(B|A)=\frac{P(AB)}{P(A)}=\frac{1/2}{2/3}=\frac{3}{4}>\frac{2}{3}
\]
所以由此看出，不应该 \(random\ spin.\)
