贝叶斯定理是个哲学问题么？

wufaxian

问题和答案我都看过了，答案的解题过程我看懂了。但是思想上还是转不过弯来。假如题目稍作改动把“我若告诉你”，改成我告诉你是B会被释放，那么此时A被释放的概率是不是1/2。是啊！从这个角度讲。看守说的没错啊！我觉得答案的解题过程都是基于“告诉”还没发生的前提下的计算！——————-以上我的认识是否正确呢？

问题
犯人的难题.已知三个犯人中有两个犯人将要被释放,但在事情还未公布之前,被释 放犯人的身份是保密的.其中一个犯人要求看守人告诉他,在他的两个狱友中哪一个将 被释放.看守拒绝了他的要求,理由如下：“在现有的信息之下,你被释放的概率为2/3. 我若告诉你这个信息,将在你和另一个犯人之间确定哪一个人被释放,所以你被释放的 概率就将变成1/2.''这个看守所列理由的错误在哪里


答案：
Intuitively, there is something wrong with this rationale. The reason is that it is not based on a correctly specified probabilistic model. In particular, the event where both of the other prisoners are to be released is not properly accounted in the calculation of the posterior probability of release.

To be precise, let A, B, and C be the prisoners, and let A be the one who considers asking the guard. Suppose that all prisoners are a priori equally likely to be released. Suppose also that if B and C are to be released, then the guard chooses B or C with equal probability to reveal to A. Then, there are four possible outcomes:

(1) A and B are to be released, and the guard says B (probability 1/3).

(2) A and C are to be released, and the guard says C (probability 1/3).

(3) B and C are to be released, and the guard says B (probability 1/6).

(4) B and C are to be released, and the guard says C (probability 1/6).

Thus,