NO.PZ2020010301000002
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.
贝叶斯公式： Pr(A|B) =Pr(B|A)Pr(A) /Pr(B)
如果A和B事件是独立的，则 Pr(B|A) = Pr(B)，因此 Pr(A|B) = Pr(A)。 A和B互相不包含彼此的信息，因此以上的条件概率带入之后，贝叶斯公式还是成立的。
如果A和B事件完全相关，则 Pr(B|A) = 1，因此 Pr(A|B) 就是概率之比，Pr(A)/Pr(B)，贝叶斯公式依旧成立。
B是A的子集，P（A｜B）才是等于1吧答案有误？
