∪ (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
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MATHEMATICS
Therefore,
P (A) = P (E1) P (A|E1) + P (E2) P (A|E2) + + P (En)P(A|En)
or
P(A) =
1
P(E )P(A|E )
n
j
j
j=∑
Example 15 A person has undertaken a construction job