In [31]:

import pandas as pd
import numpy as np

In [43]:

toy_dataset = pd.read_csv('toy_dataset.csv')
toy_dataset.head()

Out[43]:

	Number	City	Gender	Age	Income	Illness
0	1	Dallas	Male	41	40367.0	No
1	2	Dallas	Male	54	45084.0	No
2	3	Dallas	Male	42	52483.0	No
3	4	Dallas	Male	40	40941.0	No
4	5	Dallas	Male	46	50289.0	No

In [22]:

toy_dataset.shape

Out[22]:

(150000, 6)

If we need the Age for the person in the row 3, we can calculate:

In [44]:

Age_3 = toy_dataset.iloc[3,3]
Age_3

Out[44]:

We saw how calculate the empirical probability, we use it to estimate the probability of union of pairs the events:

A={The person chosen lives in San Diego}

B={The person chosen is Male}

C={The person chosen has a income of 78898.0}

In [45]:

def person():
    return np.random.randint(0,149999)

In [54]:

def empirical_prob(n=10000):
    positive_cases = 0
    for i in range(n):
        pick = person()
        if toy_dataset.iloc[pick,1] == "San Diego" or toy_dataset.iloc[pick,2] == "Male":
            positive_cases +=1
    return positive_cases/n
empirical_prob()

Out[54]:

0.57384

let's calculate the theoretical probability of $A\cup B$

In [62]:

data_A= toy_dataset[toy_dataset["City"] == "San Diego"]
data_B= toy_dataset[toy_dataset["Gender"]=="Male"]
data_C=  toy_dataset[toy_dataset["Income"]==78898.0]
data_AnB = toy_dataset[(toy_dataset["City"] == "San Diego") & (toy_dataset["Gender"]=="Male")]
(data_A.shape[0]+data_B.shape[0]-data_AnB.shape[0])/150000

Out[62]:

0.5726533333333333

Another way

In [64]:

data_AB = toy_dataset[(toy_dataset["City"] == "San Diego") | (toy_dataset["Gender"]=="Male")]
data_AB.shape[0]/150000

Out[64]:

0.5726533333333333

Do the same for the other cases

In [ ]:

In [47]:

def empirical_prob(n=10000):
    positive_cases = 0
    for i in range(n):
        pick = person()
        if toy_dataset.iloc[pick,2] == "Male" or toy_dataset.iloc[pick,4] == 78898.0: 
            positive_cases +=1
    return positive_cases/n
empirical_prob()

Out[47]:

0.5767

In [55]:

data_BC = toy_dataset[(toy_dataset["Gender"]=="Male") | (toy_dataset["Income"]==78898.0)]
data_BC.shape[0]/150000

Out[55]:

0.5586733333333334

In [65]:

data_B= toy_dataset[toy_dataset["Gender"]=="Male"]
data_C=  toy_dataset[toy_dataset["Income"]==78898.0]
data_CnB = toy_dataset[(toy_dataset["Gender"]=="Male") & (toy_dataset["Income"]==78898.0)]
(data_B.shape[0]+data_C.shape[0]-data_CnB.shape[0])/150000

Out[65]:

0.5586733333333334

In [48]:

def empirical_prob(n=10000):
    positive_cases = 0
    for i in range(n):
        pick = person()
        if toy_dataset.iloc[pick,1] == "San Diego" or toy_dataset.iloc[pick,4] == 78898.0: 
            positive_cases +=1
    return positive_cases/n
empirical_prob()

Out[48]:

0.0323

In [56]:

data_AC = toy_dataset[(toy_dataset["City"] == "San Diego") | (toy_dataset["Income"]==78898.0)]
data_AC.shape[0]/150000

Out[56]:

0.03254666666666667

In [66]:

data_A= toy_dataset[toy_dataset["City"] == "San Diego"]
data_C=  toy_dataset[toy_dataset["Income"]==78898.0]
data_AnC = toy_dataset[(toy_dataset["City"] == "San Diego") & (toy_dataset["Income"]==78898.0)]
(data_A.shape[0]+data_C.shape[0]-data_AnC.shape[0])/150000

Out[66]:

0.03254666666666667

In [ ]:

MguadapvMguadapv

The Addition Rule