Bayes' theorem

conditional probability

A/B are event, when B happen, A‘s conditional probability. ps.P(B) > 0

NB_3.png

seven ball in p1 p2
two white ball in p1
one white ball in p2
What’s the probability when fetch white from B bucket.

Event A is fetch white
Event B is fetch from P2 bucket

Multiplication formula

  1. formula

  2. when n >= 2 :

  3. full probability formula
    if event array B1, B2, B3, … satisfying

  • i ≠ j
  • i,j=1 2 ….

then array event is a divide of sample space Ω .

this formula mean no interference event array can calculate target sample space in divide.
It’s called prior probability

For example: spot check a set of different products’ good rate

bayes formula

bayes formula is the reverse process of full probability formula.
It research a happened event cause factor, not forcast it.
It’s called posterior probability

For example:
find killer in criminal suspect
spam filtering in e-mail system

https://www.cnblogs.com/ohshit/p/5629581.html