# 概率问题贝叶斯定理推导与误区

$P(A) \ P(B|A) = P(B) \ P (A|B)$

$\ P (A|B) = \frac{P(A) \ P(B|A)}{P(B) }$

$P(A|B) = \frac{\frac{1}{1000}\ \times 0.99} { \frac{1}{1000} \ \times 0.99} =\%100$

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To sum up Bayes' Theorem, can we not think like the following way:
1. A test != An event
2. Tests are not 100% accurate.
3. A test can only give us the probability of its own, but NOT the actual probability.
4. There are false positives skewing the test results.

Therefore, to extract the real probability from a test, we need to -
1. Know the probabilities of false positive and false negative.
2. Base the real probability on the test probability.

E.g.
a. We have a drug test result.
b. We need to get the known error rates.
c. We may get the actual chance of positive.

Wavelet: To sum up Bayes' Theorem, can we not think like the following way:
1. A test != An event
2. Tests are not 100% accurate.
3. A test can only give u ...

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