# 三人成虎和贝叶斯公式

$$P(H|E)=\frac{P(E|H)P(H)}{P(E)}$$

$$P(E)=P(E|H)P(H)+P(E|¬H)P(¬H)$$

$$P(H|E)=\frac{P(E|H)P(H)}{P(E)}=\frac{0.9\times0.01}{ 0.9\times0.01 + 0.1\times0.99 }=\frac{1}{12}=0.08333…$$

$$P(H|E)=\frac{P(E|H)P(H)}{P(E)}=\frac{0.9\times\frac{1}{12}}{ 0.9\times \frac{1}{12} + 0.1\times \frac{11}{12}}=0.45$$

$$P(H|E)=\frac{P(E|H)P(H)}{P(E)}=\frac{0.9\times0.45}{ 0.9\times 0.45 + 0.1\times 0.55}=0.88…$$

$$P(H|E)P(E)=P(E|H)P(H)$$

100个人中有10个罪犯. 已知10个罪犯中，有5个是穿红衣服，有8个穿白袜子。这一百个人中，有10个人穿红衣服，有45个穿白袜子，请问一个概率，遇到一个红衣服白袜子的人，多大的可能这人是个罪犯？

## LaTex support (2020)

I used to use jsMath to support latex in this website, but it no longer works (I have no idea why). The one I am using right now in this blog is MathJax LaTex WordPress plugin. A pleasant surprise is that my old equations (e.g. in Balloon model) stil

When I was in high school and saw the following equation, my mind was blown! $$1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+…=\frac{\pi^2}{6}$$ Why is Pi here? Isn’t it supposed to show up only in circle related problem? But the left-hand has n