Drawing Marbles

Evan has a bag with 2 red marbles and 2 blue marbles. He also has a stack of infinite red and blue marbles beside him. Evan draws two marbles at random and puts either a red or blue marble back based on the following conditions:

(A) If the marbles are the same color, Evan puts a marble of the opposite color back in the bag. (ex. if he draws two red marbles, he puts a blue one back from his infinite pile of marbles)

(B) If the marbles are different colors, Evan puts the blue marble back in the bag.

If Evan repeats this process until there is one marble left, the probability that it is red can be written as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

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