You download two sets of posts from an online forum. Set One isa collection of posts by \"pro-Hong Kong Protestors\" (HKP) students.Set Two is a collection of posts by pro-Chinese Government (CG)students. (Let's say you get these two collections by searching forstudents who are members either of a pro-HKP group, or pro-CGgroup.) You compute the probabilities of different words they use,and focus on a set of six \"key\" words of interest, {\"legal\",\"democracy\", \"violence\", \"legitimate\", \"calm\", \"foreign\"}. Youcompute the \"probability that, given that they use one of thesefive words, which word it is\" (you could do this by counting upeach of those words for the two sets, and dividing by the totalnumber of those words in each set.) words: {\"legal\", \"democracy\",\"violence\", \"legitimate\", \"calm\", \"foreign\"}. pHKP = {0.2, 0.2,0.3, 0.2, 0.05, 0.05} pCG = {0.1, 0.05, 0.3, 0.05, 0.1, 0.4}

The government tells you that they think about 10% of theposters on the mainland are pro-HKP, and they just want to have aconversation with these people about things.

You encounter a post. The poster uses the word \"democracy\" twice,the word \"violence\" once, and the word \"foreign\" once. Assumingthat he is either pro-HKP, and follows the pHKP distribution, orpro-CG, and follows the pCG distribution...

Q: Given government priors, what is the probability that theposter is pro-HKP? (i.e., follows the pHKP distribution rather thanthe pCG distribution)