# Bayes’ Theorem in Plain English

## Simplest explanation of Bayes’ Theorem

3 min readNov 4, 2021

Assume we have a hypothetical machine learning model that has been used to obtain predicted class values (**class 0** and **class 1**) as shown in **Table 1** below.

Our system is a binary system with 2 classes, that is, **class 0** and **class 1, **with a total of 10 rows.

Let’s start by defining some basic probabilities (n = 10):

where

*P(Ye = 1)*is the probability that the**exact**value*Ye*is 1*P(Ye = 0)*is the probability that the**exact**value*Ye*is 0*P(Yp = 1)*is the probability that the**predicted**value*Yp*is 1*P(Yp = 0)*is the probability that the**predicted**value is*Yp is*0

## Bayes’ Theorem for Class 1

Now let us focus on the **class 1**, then from T**able 1** above, we define the following conditional probabilities: