07 Addition rule for probability

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import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
from matplotlib_venn import venn2
import seaborn as sns

khanacademy

bag = 8 * ['Green-Cube'] + 9 * ['Green-Sphere'] + 5 * ['Yellow-Cube'] + 7 * ['Yellow-Sphere']

def P(cond, total_lst):
    cond_lst = list(filter(cond, total_lst))
    return len(cond_lst) / len(total_lst), cond_lst

# P(Cube)
p_cube, p_cube_lst = P(lambda x: x.endswith('Cube'), bag)
print(p_cube)

0.4482758620689655

# P(Yellow)
p_yellow, p_yellow_lst = P(lambda x: x.startswith('Yellow'), bag)
print(p_yellow)

0.41379310344827586

# P(Yellow And Cube)
p_yellow_and_cube, _ = P(lambda x: x.startswith('Yellow') and x.endswith('Cube'), bag)
print(p_yellow_and_cube)

0.1724137931034483

# P(Yellow or Cube)
p_yellow_or_cube, _ = P(lambda x: x.startswith('Yellow') or x.endswith('Cube'), bag)
print(p_yellow_or_cube)

0.6896551724137931

P(A OR B) = P(A) + P(B) - P(A AND B)

# P(Yellow or Cube) = P(Yellow) + P(Cube) - P(Yellow And Cube)
p_yellow_or_cube == p_yellow + (p_cube - p_yellow_and_cube) # find the reason why

True

def intersection(lst1, lst2): 
    lst3 = [value for value in lst1 if value in lst2] 
    return lst3 

p_yellow_interset_p_cube_lst = [val for val in p_yellow_lst if val in p_cube_lst]

venn2(subsets=[len(p_cube_lst),
               len(p_yellow_lst),
               len(p_yellow_interset_p_cube_lst)],
     set_labels=['Cubes', 'Yellow'],
     set_colors=['Blue', 'Yellow'])

<matplotlib_venn._common.VennDiagram at 0x7feabbbc6e50>