(a) Events A and B are such that P ( A )=1/2, P ( B )=7/12 and P (Ā ∪ B̄)=1/4 Find whether the events A and B are independent or not.

Events A and B are such that \[\mathrm{P}(\mathrm{~A})=\frac{1}{2}, \mathrm{P}(\mathrm{~B})=\frac{7}{12} \text { and } \mathrm{P}(\overline{\mathrm{~A}} \cup \overline{\mathrm{~B}})=\frac{1}{4} \] Find whether the events $\displaystyle A$ and $\displaystyle \mathrm{B}$ are independent or not.

A box $\displaystyle \mathrm{B}_{1}$ contains $\displaystyle 1$ white ball and $\displaystyle 3$ red balls. Another box $\displaystyle \mathrm{B}_{2}$ contains $\displaystyle 2$ white balls and $\displaystyle 3$ red balls. If one ball is drawn at random from each of the boxes $\displaystyle \mathrm{B}_{1}$ and $\displaystyle \mathrm{B}_{2}$, then find the probability that the two balls drawn are of the same colour.