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If A and B are events with P(A) ≠ 0 and P(B) ≠ 1, then the value of P(Ā | B̄) is:

1. 1 - P(A | B)
2. 1 - P(Ā | B̄)
3. 1 - P(A ∪ B) / P(B̄)
4. P(Ā) / P(B̄)

Correct answer: 1 - P(A ∪ B) / P(B̄)

Solution

P(A'|B') = P(A' ∩ B')/P(B') = P((A∪B)')/P(B') = (1 - P(A∪B))/P(B'). The option P(A')/P(B') can exceed 1 and is invalid, while 1 - P(A∪B)/P(B') (read as the standard NCERT form) gives the correct value.

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