# For $k= 1,2,3$ the box $B_k$ contains k red balls and $(k+1)$ white balls. Let $P(B_1)-\large\frac{1}{2}$$, P(B_2)-\large\frac{1}{3}$ and $P(B_3)=\large\frac{1}{6}$. A box is selected at random and a ball is drawn from it . If a red ball is drawn, then the probability that it has come from box $B_2$ is

$\begin {array} {1 1} (1)\;\frac{35}{78} & \quad (2)\;\frac{14}{39} \\ (3)\;\frac{10}{13} & \quad (4)\;\frac{12}{13} \end {array}$