Box A contains 2 black and 3 red balls, white Box contains 3 black and 4 red balls. Out of these two boxes one is selected at random ; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B, is :

Question

$$\begin {array} {1 1} (a)\; \frac{21}{41} & \quad (b)\;\frac{10}{31} \\ (c)\;\frac{12}{31} & \quad (d)\;\frac{13}{41} \end {array}$$