This Probability Puzzle Has a Genius Solution

You have a bag that contains 10 red balls, 20 green balls and 30 blue balls.
You remove balls one at a time until there are no balls left.
What is the probability that there is at least one blue ball and at least one green ball remaining when you take the last red ball?
We'll use a couple of really neat tricks to make this probability puzzle a lot easier than it looks!
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[@patrickludden]

brilliant concept.
by changing the way we look at the problem it goes from being a long / time consuming route to the solution to a much neater and quicker route.

[@Mathsaurus]

Thanks!