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A stick is 5 units long. It is broken at two points, chosen at random. What is the probability that all three pieces are longer than 1 unit?

There was the ame question, but there was no correct answer.

 Feb 8, 2020
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When we break off the first piece, the probability that the first piece will be longer than 1 unit is 3/5.  (This is because we look at the stick as the interval [0,5], then we can break the stick anywhere between 1 and 4.)  We are now left with a stick with a length of 4.  When we break off the second piece, the probability that the second piece will be longer than 1 is 2/4 = 1/2.  This can happen at either end, so the answer is 2*3/5*1/2 = 3/5.

 Feb 8, 2020

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