Question
Download Solution PDFIf P(A ∪ B) = P(A ∩ B) for any two events A and B, then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
P(A) + P(B) - P(A ∩ B) = P(A ∪ B)
Calculation:
As; P(A ∪ B) = P(A ∩ B)
And, putting this value in the formula we get
⇒ P(A) - P(A ∩ B) + P(B) - P(A ∩ B) = 0 ----(1)
⇒ P(A) - P(A ∩ B) ≥ 0
⇒ P(B) - P(A ∩ B) ≥ 0
So, P(A) - P(A ∩ B) + P(B) - P(A ∩ B) ≥ 0 ----(2)
From (1) and (2), we get
⇒ P(A) - P(A ∩ B) = 0 and P(B) - P(A ∩ B) = 0
⇒ P(A) = P(A ∩ B) and P(B) = P(A ∩ B)
⇒ P(A) = P(B)
∴ The relation is P(A) = P(B).
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