question_answer

For k= 1, 2, 3 the box \[{{B}_{k}}\]contains k red balls and\[(k+1)\] white balls. Let \[P({{B}_{1}})=\,\frac{1}{2},P({{B}_{2}})=\frac{1}{3}\] and \[P({{B}_{3}})=\,\frac{1}{6}.A\] 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

A)  \[\frac{35}{78}\]                      

B)  \[\frac{14}{39}\]

C)  \[\frac{10}{13}\]                      

D)  \[\frac{12}{13}\]