Not as easy as it looks (Part 2)

Bag X contains 4 red marbles, 7 blue marbles, and 8 green marbles. Bag Y contains 12 red marbles, 4 blue marbles, and 9 green marbles. Bag Z contains 13 red marbles, 5 blue marbles, and 7 gray marbles. I choose a bag at random, and a marble from the bag. Given that the marble is green, the probability that the marble was from Bag Z is \(p\). Compute \(\lfloor{100p}\rfloor\).

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