John has three bags that each contain 500 marbles. Bag 1 has 14 red marbles, 461 green marbles, and 25 yellow marbles. Bag 2 has 184 blue marbles, 56 pink marbles, and 260 red marbles. Bag 3 has 75 orange marbles, 234 red marbles, 191 blue marbles. John randomly chooses one of the bags at random and then randomly pick a marble from the chosen bag. What is the probability that the John's chosen marble is red? Round your answer to three decimal places.

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