In [1]:

import pandas as pd

Probabilities Add Up to 1¶

Another important property we are going to learn is that the probabilities of events that make the whole sample space will add up to $1$. For example:

In [2]:

dataset =  pd.DataFrame({
    'Person #':[1,2,3,4,5,6,7,8,9,10],
    'City':['SF','SF','NY','NY','NY','SF','NY','SF','SF','SF'],
    'Age':[41,26,28,53,32,51,65,49,25,33]
})
dataset

Out[2]:

	Person #	City	Age
0	1	SF	41
1	2	SF	26
2	3	NY	28
3	4	NY	53
4	5	NY	32
5	6	SF	51
6	7	NY	65
7	8	SF	49
8	9	SF	25
9	10	SF	33

In [3]:

dataset.sample(1)['City'].values[0]

Out[3]:

'SF'

In this experiment, if we think of the events $E=$ "the person chosen is from SF" and $F=$ "the person chosen is from NY", we can notice that toghether they make the whole sample space $\Omega=\{SF,NY\}$.

So, even though we don't know yet how much each probability is, we can tell that:

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1.7. Probabilities Add Up to 1

Probabilities Add Up to 1¶

$P(E)+P(F)=1$.¶

	Person #	City	Age
0	1	SF	41
1	2	SF	26
2	3	NY	28
3	4	NY	53
4	5	NY	32
5	6	SF	51
6	7	NY	65
7	8	SF	49
8	9	SF	25
9	10	SF	33

	Person #	City	Age
0	1	SF	41
1	2	SF	26
2	3	NY	28
3	4	NY	53
4	5	NY	32
5	6	SF	51
6	7	NY	65
7	8	SF	49
8	9	SF	25
9	10	SF	33

	Person #	City	Age
0	1	SF	41
1	2	SF	26
2	3	NY	28
3	4	NY	53
4	5	NY	32
5	6	SF	51
6	7	NY	65
7	8	SF	49
8	9	SF	25
9	10	SF	33