The chances of a defective screw in three boxes A, B, and C are 15, 16,   and 17​ respectively. A box is selected at random and a screw drawn from it at random is found to be defective. What is the probability that it came from box A?

Box A contains 2 black and 3 red balls, while Box B contains 3 black and 4 red balls. One of these two boxes 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 what is the probability that it came from box B?