Bayes' Theorem with solved examples | Statistics

In Statistics, Bayes’ Theorem is a very important theorem that has a
wide range of applications in real-life situations. It is also called the
fundamental theorem of Statistics which is based on conditional
probabilities.
The Bayes’ Theorem is easy to apply and convenient for computational
purposes.
Let’s start the Bayes’ Theorem!



Bayes’ Theorem
Introduction to Bayes’ Theorem :
In mathematical statistics, the Bayes’ Theorem is named after the
greatest statistician Sir Thomas Bayes. The Bayes’ Theorem tells us
about the probability of an event, about which we have some earlier
knowledge of the conditions related to that event.
For example, the risk of failure of a car machine increases with the age
of the car. So, Bayes’ Theorem allows us to measure the risk, that is
what is the probability that the machine will fail after provided age.
Mathematical Statement of Bayes’ Theorem :
We can state the Bayes’ Theorem mathematically as follows;
P (B∨ A) P (A )
P(A|B)= P(B)



 Where A and B are events and P(B)≠0
 P(A|B) and P(B|A) are conditional probabilities are we can read
them as, ‘Probability of occurrence of event A given event B is