, n
Proof By formula of conditional probability, we know that
P(Ei|A) = P(A
E )
P(A)
i
∩
= P(E )P(A|E )
P(A)
i
i  (by multiplication rule of probability)
=
1
P(E )P(A|E )
P(E )P(A|E )
i
i
n
j
j
j=∑
 (by the result of theorem of total probability)
© NCERT
not to be republished
PROBABILITY      551
Remark  The following terminology is generally used when Bayes' theorem is applied The events E1, E2, , En are  called hypotheses The probability P(Ei) is called the priori probability of the hypothesis Ei
The conditional probability P(Ei |A) is called a posteriori probability of the
hypothesis Ei