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Let’s say that we have a stick of length L and we break it up into...

Let’s say that we have a stick of length L and we break it up into 3 pieces randomly. Here random means that we sample two numbers a, b from the uniform continuous distribution on [0, L] such that 0 < a < b < L (If a turns out to be bigger than b, we can always rename them). So now we have three pieces, [0, a], [a, b] and [b, L]. What is the probability that these three broken pieces form a triangle?

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