pistol brain teaser

某银行面世我时, INTERVIEWR (老印, 很NICE)我以下一个问题, 至今不明白我错了:
一歹徒持一有2发子弹（2子弹紧挨）的手枪, 其CHAMBER为圆形,具有6个腔。歹徒刚用
向某人开了一枪，被射击者侥幸逃得一命因为此时腔中无子弹。现歹徒顶住你的头，给
你两个选择：
1）接过枪草自己开一枪；
2）Randomize Chamber, then shoot yourself
问：何种情况你的存活率高？
谢谢！！
我选了（2）

should be (1)
set x = 1, or 0.

set P(x = 1|x = 0) = p(x=0|x=1)*p(x=1)/p(x=0) = 5/6*1/3/(2/3) = 5/12
obviously in (2) P =2/6 = 1/3

Up to here, the conclusion is obvious: (2) is better cause we have less probability of shotting a
bullet.

But that's not the answer: cause p(x=0|x=1) is not like 5/6. It is c(6, 2) = 1/2. So the P(x=1|x=0) = 1/2*1/3/(2/3) = 1/4

So the answer is (1)