Engineering
Mathematics
Addition Theorem on Probability
Question
For any two events A and B
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Solution
∵ P(A∪B) = P(A) + P(B) − P(A∩B)
on rearranging we get
P(A∩B) = P(A) + P(B) − P(A∪B) which is option (C)
Also ∵ 0 ≤ P(A∪B) ≤1
⇒ P(A) + P(B) − 1 ≤ P(A∩B) ≤ P(A) + P(B)
Hence A is also correct
Now if P(A∩B) = P(A) + P(B) + P(A∩B)
⇒ P(A) + P(B) = 0
which is not necessary for the events A and B