Bayes Theorem Formula:

Bayes theorem is also known as the formula for the probability of causes.It is used to determine the conditional probability of the given event.Conditional probability is defined as the likelihood that an event will occur, based on the occurrence of a previous outcome.

P(A|B) = P(B|A) . P(A)P(B)

Where,

P(A)= The probability of occurrence of event A.

P(B)= The probability of occurrence of event B.

P(A|B) is the probability of event A given B.

P(B|A) is the probability of event B given A.

P(A∩B) is the probability of occurrence of both A and B.

Bayes Theorem Proof :

Terminologies used in Bayes Theorem :

Hypotheses: The events E₁, E₂,... E_n is called the hypotheses.

Priori Probability: The probability P(E_i) is considered as the priori probability of hypothesis E_i

Posteriori Probability: The probability P(E_i|A) is considered as the posteriori probability of hypothesis E_i