问题如下：
Can Bayes’ rule be helpful if A and B are independent? What if A and B are perfectly dependent so that B is a subset of A?
解释：
Bayes’ rule says that Pr(A|B) =Pr(B|A)Pr(A) /Pr(B)
If these events are independent, then Pr(B|A) = Pr(B) so that Pr(A|B) = Pr(A). B has no information about A and so updating with Bayes’ rule never changes the conditional probability.
If these events are perfectly dependent, then Pr(B|A) = 1, so that Pr(A|B) is just the ratio of the probabilities, Pr(A)/Pr(B).
Here the probability also only depends on unconditional probabilities and so never changes.
所以结论是：两件事情，独立和完全相关都不会影响贝叶斯规则。出题一般都有补充前提条件“假设xx独立”，没有看到过“假设xx完全相关”。如果是后者，大概会以什么形式出题呢？