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What is the probability that if you break a stick at $2$ points the three sides form a triangle?

Is there a technique that avoids calculus?

Turbo
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    Depends. How do you choose the two points? – Brian Tung Jul 14 '16 at 20:51
  • Assuming you choose the two break points points uniformly, this is a well known problem. Several different solutions can be found here – lulu Jul 14 '16 at 20:52
  • @BrianTung case $1$ uniformly random independently and case $2$ pick one point uniformly randomly and pick one of two broken sticks and pick one point uniformly randomly on that stick – Turbo Jul 14 '16 at 20:52
  • @Turbo You should add that to the question. It's not the standard and leads to a different answer. A discussion of the variants (including yours) can be found here – lulu Jul 14 '16 at 21:07
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    Your specific variant is also discussed here – lulu Jul 14 '16 at 21:10
  • All three segments can form a triangle, every single time. Are you looking for a particular type of triangle? – Pete Mancini Jul 14 '16 at 22:22

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