Articles → MACHINE LEARNING → Bayes Theorem In Machine Learning

Bayes Theorem In Machine Learning

This article describes Bayes’ theorem.

Probability

Let us discuss the basics first. Probability is the measure of how likely an event is to happen.

Probability always lies between 0 and 1.

0 = impossible event
1 = certain event

Formula Of Probability

The formula for calculating probability is: -

Picture showing the formula of calculating probability

Probability of getting a 3 = 1/6
Probability of getting an even number = 3/6=0.5

Independent And Dependent Events

Independent events are those in which one event does not affect the other. For example, tossing two coins is an independent event.

Dependent events are those in which one event affects the other. For example, a bag has two balls (one red and one blue). You pick a ball from the bag. The probability of getting the second ball as red depends on the color of the first ball.

Joint Probability

The probability that two events happen together is the joint probability. If A and B are two events, then the formula for calculating the joint probability is: -

P(A)×P(B)

For example, the probability of rolling a 2 on the dice and flipping heads on a coin is: -

1/6 X 1/2 = 1/12

Union

The probability that either event happens. If A and B are events, then the formula for calculating the union is: -

P(A)+P(B)−P(A∩B)

Where P(A∩B) is the joint probability. For example, the probability of an even number OR a multiple of 3.

A: Even number = {2, 4, 6}
B: Multiple of 3 = {3, 6}
P(A) = 3/6 = 1/2
P(B) = 2/6 = 1/3
P(A∩B) = (1/2 X 1/3) = 1/6

Union = 1/2 + 1/3 – 1/6 = 2/3 = 66.7%

Conditional Probability

If A and B are events, the probability of A happening given that B has already happened. The formula for calculating the conditional probability is: -

Consider the following example - Imagine a shopping mall with 100 customers. 40 of them entered the electronics section. Out of those 40, 10 customers bought a laptop.

P(B) = 40/100 = 0.4
P(A∩B) = 10/100 = 0.1
P(A|B) = 0.1/0.4 = 0.25

Bayer’S Theorem

Bayes’ theorem tells us how to update our belief (probability) about an event when new evidence comes in. The formula is: -

Parameter	Description
P(A)	Probability of an event before seeing evidence (called prior probability).
P(B)	New evidence
P(B\|A)	The likelihood: how probable it is to observe the evidence B if A were true.
P(A\|B)	Updated probability after observing the evidence B (called Posterior probability).

Posted By -	Karan Gupta

Posted On -	Thursday, September 25, 2025

Query/Feedback

Your Email Id		**

Subject		*

Query/Feedback	Characters remaining 250	**