Bayes' theorem is a way to calculate conditional probability and update beliefs based on evidence. It states that the probability of an event A given event B is the probability of B given A multiplied by the probability of A, divided by the probability of B. The theorem is demonstrated through an example where a doctor uses it to calculate the probability that a patient with stiff neck has meningitis based on known conditional probabilities of symptoms and disease prevalence. Bayes' theorem is useful in science and many applications because it provides a framework for revising hypotheses based on new empirical evidence or data.

1. DIL AFROSE
ESHA
ID: 161002074
DEPARTMENT OF
CSE

2. CONTENT
Bayes’ Theorem
The Formula
Bayes’ Theorem Example
 Why is Bayes’Theorem socool?

3. WHAT IS BAYES’ THEOREM?
The theorem was named after English mathematician
Thomas Bayes (1701-1761).
Bayes’ theorem is a way to figure out conditional
probability.
Conditional probability is the probability of an event
happening, given that it has some relationship to one
or more other events.
01
Definition

4. The Formula
Bayes’ Theorem (also known as Bayes’ rule). The formal definition for the
rule is:
02

5. BAYES’ IN
ACTION
A Doctor knows that disease meningitis causes the patient to have a
stiff neck, say 50% of the time.The doctor also knows some
unconditional facts: the prior probability that a patient has meningitis
is 1/50,000, and the prior probability that any patient has a stiff neck
is 1/20. Let s be the proposition that the patient has a stiff neck and
m be the proposition that the patient has meningitis.What is the
probability of having disease meningitis due to stiff neck.
Example
03
Solution

6. BAYES’ IN ACTION
04

7. BAYES’ IN ACTION
05

8. BAYES’ IN ACTION
06

9. BAYES’ IN ACTION
07

10. WHY IS BAYES’ THEOREM SO
COOL?
Describes what makes something "evidence" and how much evidence it
is.
Science itself is a special case of Bayes’ theorem because you are
revising a prior probability (hypothesis) in the light of an observation or
experience that confirms your hypothesis (experimental evidence) to
develop a posterior probability(conclusion)
Used to judge statistical models and widely applicable in
computational biology, medicine, computer science, artificial
intelligence, etc.
08

11. HELP SITE
1. https://en.wikipedia.org/wiki/Bayes%27_theorem
2. https://www.youtube.com/watch?v=VQl5_K7V44g&t=391s
3. https://www.slideshare.net/sabareeshbabu/bayes-theorem-
4406796