*26*

The **conditional probability** that event *A* occurs, given that event *B* has occurred, is calculated as follows:

P(A|B) = P(Aâˆ©B) / P(B)

where:

P(Aâˆ©B) = the probability that eventÂ *AÂ *and eventÂ *BÂ *bothÂ occur.Â

P(B) = the probability that event B occurs.

The following example shows how to use this formula to calculate conditional probabilities in Python.

**Example: Calculate Conditional Probability in Python**

Suppose we send out a survey to 300 individuals asking them which sport they like best: baseball, basketball, football, or soccer.

We can create the following table in Python to hold the survey responses:

import pandas as pd import numpy as np #create pandas DataFrame with raw data df = pd.DataFrame({'gender': np.repeat(np.array(['Male', 'Female']), 150), 'sport': np.repeat(np.array(['Baseball', 'Basketball', 'Football', 'Soccer', 'Baseball', 'Basketball', 'Football', 'Soccer']), (34, 40, 58, 18, 34, 52, 20, 44))}) #produce contingency table to summarize raw data survey_data = pd.crosstab(index=df['gender'], columns=df['sport'], margins=True) #view contingency table survey_data sport Baseball Basketball Football Soccer All gender Female 34 52 20 44 150 Male 34 40 58 18 150 All 68 92 78 62 300

**Related**: How to Use pd.crosstab() to Create Contingency Tables in Python

We can use the following syntax to extract values from the table:

#extract value in second row and first column survey_data.iloc[1, 0] [1] 34

We can use the following syntax to calculate the probability that an individual is male, given that they prefer baseball as their favorite sport:

#calculate probability of being male, given that individual prefers baseball survey_data.iloc[1, 0] / survey_data.iloc[2, 0] 0.5

And we can use the following syntax to calculate the probability that an individual prefers basketball as their favorite sport, given that theyâ€™re female:

#calculate probability of preferring basketball, given that individual is female survey_data.iloc[0, 1] / survey_data.iloc[0, 4] 0.3466666666666667

We can use this basic approach to calculate any conditional probability weâ€™d like from the contingency table.

**Additional Resources**

The following tutorials provide additional information on dealing with probability:

Law of Total Probability

How to Find the Mean of a Probability Distribution

How to Find the Standard Deviation of a Probability Distribution