Thus,
P(A) = P [(A ∩ E1) ∪ (A ∩ E2)∪ ∪ (A ∩ En)]
= P (A ∩ E1) + P (A ∩ E2) + + P (A ∩ En)
Now, by multiplication rule of probability, we have
P(A ∩ Ei) = P(Ei) P(A|Ei) as  P (Ei) ≠ 0∀i = 1,2, , n
© NCERT
not to be republished
 550
MATHEMATICS
Therefore,
P (A) = P (E1) P (A|E1) + P (E2) P (A|E2) +