If E1 , E2 , E3 .....En are n non empty events which constitute a partition of sample space S, i.e.
E1, E2 ,...En are pairwise disjo int & E1, ∪ E2 ... ∪ En = S and A is any event of nonzero probabilit y, then
for any i= 1, 2, 3,.... n
Proof: By formula of conditional probability, we know that
By multipication rule of probability
(by total prob.theo.)
Note: The events E1, E2, E3, En, are called hypotheses The probabilit y P(E )is called the priori probabilit y of the hypothesis Ei
The conditiona l probabilit y P(Ei /A) is called a posteriori probabilit y of the hypothesis hypothesis Ei.
