**Given:** A and B are the events such that P(A) = \(\frac{1}{2}\) and P(B) = \(\frac{7}{12}\) and

P(not A or not B) = \(\frac{1}{4}\)

**To Find: **

**(i)** If A and B are mutually exclusive

Since P(not A or not B) = \(\frac{1}{4}\) i.e., P\((\overline A\cup\overline B)\) = \(\frac{1}{4}\)

we know that , P\((\overline A\cup\overline B)\)) = P(A ∩ B)' = 1 - P(A ∩ B) = 0

But here P(A ∩ B) \(\neq\) 0

Therefore , A and B are not mutually exclusive.

**(ii)** If A and B are independent

The condition for two events to be independent is given by

P(E_{1} ∩ E_{2}) = P(E_{1}) x P(E_{2})

= \(\frac{1}{2}\times \frac{7}{12}\)

= \(\frac{7}{24}\) Equation 2

Since Equation 1 \(\neq\) Equation 2

\(\Rightarrow\) A and B are not independent