Naive Bayes Cookie Problem

cookie_bayes.py

'''
    
            P(A) * (B|A)
  P(A|B) = -------------- - Bayes Probability
                P(B)   

  Cookie Problem that can be solved with Bayes Probability:
  
  You are given two jars of cookies, jar 1 has 30 vanilla and 10 chocolate cookies,
  jar 2 has 20 vanilla and 20 chocolate cookies.
  You randomly pick a cookie from one of the jars and it is vanilla.
  What is the probability that it came from the first jar? P(jar 1 | vanilla)
 
  To answer this question we will use bayes framework, which involves prior knowledge
  and likelihood of event happening.
  
                        P(jar 1) * P(vanilla | jar 1)
  P(jar 1 | vanilla) = ---------------------------------
                                  P(vanilla)
                                  
  P(jar 1) = 0.5
  P(vanilla| jar 1) = (0.75 * 0.5) / 0.5 = 0.75 (joint probability: P(B|A) = P(B and A) / P(A))
  P(vanilla) = 0.5 * 0.75 + 0.5 * 0.5 = 0.625
  
  P(A|B) = (0.5 * 0.75) / 0.625 = 0.6
  
  ANSWER: probability that vanilla cookie came from jar 1 is 60%
  
'''