It is given that P(A) = \(\frac12\), P(B) = \(\frac7{12}\) and \(P( A'\cup B')\) = \(\frac14\).
⇒ \(P( A'\cup B')= \frac14\)
⇒ \(P((A\cap B)')= \frac14\) \([A'\cup B' = (A\cap B)']\)
⇒ \(1-P(A\cap B)= \frac14\)
⇒ \(P(A\cap B)= \frac34\) ......(1)
However, P(A) ⋅ P(B) = \(\frac 12.\frac7{12} = \frac7{24}\) .....(2)
Here, \(\frac34 \ne \frac7{24}\)
∴ P(A ∩ B) \(\ne\) P(A) ⋅ P(B)
Therefore, A and B are not independent events.