Each of three bags b1, b2, b3 contains only red and blue balls in the quantities:

Bag b1

red = 2 balls

blue = x2 – 6x + 13 balls

Bag b2

red = 3 balls

blue = x2 – 6x + 12 balls

Bag b3

red = 4 balls

blue = x2 – 6x + 11 balls

A ball is drawn at random from a randomly chosen bag. What is the maximum probability the drawn ball is red?