# 有誰可以教我這題? (條件機率/貝式網路)

At a certain stage of a criminal investigation, the inspector in charge is 60% convinced of the guilt of a certain suspect. Suppose now that a new piece of evidence that shows that the criminal has a certain characteristic (such as left-handedness, baldness, brown hair, etc.) is uncovered. If 20% of the population possesses this characteristic, how certain of the guilt of the suspect should the inspect now be ifit turns out that the suspect is among this group?

Let us now suppose that the new evidence is subject to different possible interpretations, and in fact only shows that it is 90% likely that the criminal possesses this certain characteristic. In this case, how likely would it be that the suspect is guilty (assuming, as before, that he has this characteristic)?

Update:

A指他有沒有罪 B指他有沒有犯人的特徵

Rating

第一題

以A表示該嫌犯有罪的事件，以B表示該嫌犯有犯人特徵的事件。我們要計算 「給定該嫌犯有犯人特徵，他有罪的機率是多少？」，也就是 P(A | B)。

P(A) = 0.6， P(AC) = 0.4，

P(B | A) = 1，也就是「給定他有罪，那他有100%的機率有犯人的特徵」。

P(B | AC) = 0.2，也就是「給定他無罪，那他有20%的機率有犯人的特徵」。

第二題

P(A) = 0.6， P(AC) = 0.4，P(B | A) = 0.9，P(B | AC) = 0.2