There is a standard problem that asks, if you randomly break a stick into three pieces, the probability that the pieces can form a triangle. The answer is not unique because there are different ways to randomly create three pieces. The method that is the most challenging to analyze breaks the stick at a random point, randomly chooses one of the pieces, and breaks it at a random point. If you can solve that puzzle you may have insight to solve the following variant:

Break a stick at a random point. Break both pieces at random points. Randomly discard one of the pieces. What is the probability the remaining pieces can form a triangle?

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There is a standard problem that asks, if you randomly break a stick into three pieces, the probability that the pieces can form a triangle. The answer is not unique because there are different ways to randomly create three pieces. The method that is the most challenging to analyze breaks the stick at a random point, randomly chooses one of the pieces, and breaks it at a random point. If you can solve that puzzle you may have insight to solve the following variant:

Break a stick at a random point. Break both pieces at random points. Randomly discard one of the pieces. What is the probability the remaining pieces can form a triangle?

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