The contest is now officially OVER
Thanks to everyone that participated, I've seen some great probabilistic thinking as well as lots of guesswork, but as always there can only be one right answer. Here are some after shots of the arena after the Roomba had its way with it, take a final guess:
After two and a half minutes, the Roomba managed to pick up.....38% of the colourful dust!
Our winner is scotty.a.simpson, with a guess of 42%. A special shout out to HKou, who was thinking along the right lines...I like your optimism, give robotics another few years and your floors will get cleaned in no time.