There are 3 bags. Bag 1 contains 2 red and a^2-4a+8 black balls, bag 2 contains 1 red and a^2-4a+9 black balls and bag 3 contains 3 red and a^2-4a+7 black balls. A ball is drawn at random from at random chosen bag. Then the maximum value of probability that is a red ball is

Question : There are 3 bags. Bag 1 contains 2 red and a^2-4a+8 black balls, bag 2 contains 1 red and a^2-4a+9 black balls and bag 3 contains 3 red and a^2-4a+7 black balls. A ball is drawn at random from at random chosen bag. Then the maximum value of probability that is a red ball is