Question

State and prove bayes theorem on probability

Answer 1

If B1, B2.......Bn are set of mutually exclusive and exhaustive events of a random even and A is another event with Bi, then P (Bi/A) = {P(Bi).P(A/ Bi)}/{(Sigma)ni=1 P Bi. P (A/ Bi).....i= 1, 2.....n

Proof:

Since, (P(ABi)=P(A∩Bi)=P(Bi).P(A/Bi)=P(A).P(Bi/A)−−−−−−−−−(1)

P(BiA)=P(Bi).P(ABi)P(A).......(2) Using total probability,

P(A)=∑i=1nPBi.P(ABi)−−−−−−(3)

 From equation 2 and 3,

P(BiA)=P(Bi).P(ABi)∑ni=1PBi.P(ABi)....... Thus Proved

Answer 2

Answer:

Step-by-step explanation:

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