Question

State and prove Baye’s theorem.

Answer 1

In probability theory and statistics, Bayes' theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

Proof of Bayes Theorem

The probability of two events A and B happening, P(A∩B), is the probability

of A, P(A), times the probability of B given that A has occurred, P(B|A).

P(A ∩ B) = P(A)P(B|A) (1)

On the other hand, the probability of A and B is also equal to the probability

of B times the probability of A given B.

P(A ∩ B) = P(B)P(A|B) (2)

Equating the two yields:

P(B)P(A|B) = P(A)P(B|A) (3)

and thus

P(A|B) = P(A)

P(B|A)

P(B)

(4)

This equation, known as Bayes Theorem is the basis of statistical inference.

Answer 2

Answer:

Explanation:

Baye's theorem states that P1 ,P2,P3,.......,Pn are the sets of mutually exclusive events that form the sample events.