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Question
If A and B are two events such that A ⊂ B and P (B) ≠ 0, then which of the following is correct?
Options
P(A|B) = `(P(B))/(P(A))`
P(A|B) < P(A)
P(A|B) ≥ P(A)
None of these
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Solution
P(A|B) ≥ P(A)
Explanation:
A ⊂ B ⇒ A ∩ B = A and P(B) ≠ 0
P(A|B) = `(P(A ∩ B))/(P(B))`
= `(P(A))/(P(B))`
P(B) ≠ 0,
∴ `(P(A))/(P(B)) < 1`
⇒ P(A) < (P(B)
∴ P(A|B) ≥ P(A)
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