Should you bring an umbrella if 3 of your friends said it will rain?

rain_bayes.py

'''
Question: You're travelling to Seattle and you've asked 3 of your friends independently if it will rain,
3 of them said it will. Each friend has 2/3 chances of being right. Should you bring an umbrella?

Assume chance of rain is 25%

                 P(rain) * P(yes | rain)
P(rain | yes) = ------------------------
                        P(yes)


P(rain) = 0.25
P(yes | rain) = P(yes and rain) / P(rain) = 0.25 * (2/3)^3 / 0.25 = 8/27
P(yes) = P(rain) * P(yes | rain) + P(no rain) * P(yes | no rain) = 0.25 * 8/27 + 0.75 * 1/27

                         0.25 * 8/27
P(rain | yes) = ----------------------------- = 0.727
                 (0.25 * 8/27 + 0.75 * 1/27)   
                 
               
'''