Understanding the math behind logistic regression

Imagine a situation where we have a dataset from a supermarket store about the gender of the customer and whether that person bought a particular product or not. We are interested in finding the chances of a customer buying that particular product, given their gender. What comes to mind when someone poses this question to you? Probability anyone? Odds of success?

What is the probability of a customer buying a product, given he is a male? What is the probability of a customer buying that product, given she is a female? If we know the answers to these questions, we can make a leap towards predicting the chances of a customer buying a product, given their gender.

Let us look at such a dataset. To do so, we write the following code snippet:

import pandas as pd
df=pd.read_csv('E:/Personal/Learning/Predictive Modeling Book/Book Datasets/Logistic Regression/Gender Purchase.csv')
df.head()

Fig. 6.1: Gender and Purchase dataset

The first column mentions...