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- Mathematical Sciences
A stick of length L is broken into two pieces at random. What is the average length of the smaller piece ?
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Eduncle Best Answer
When we break the stick into two pieces at a point x, we will be left with one piece of length x and a second piece of length L - x.
Since their lengths add up to L, whatever the choice of x, one piece will always be less than L/2, and the other greater than L/2.
So, the smaller piece will have a length ranging from 0 to L/2.
If the break point x is uniformly distributed throughout the length of the stick, then we are taking the average of 0 and L/2, so the average length of the smaller piece is L/4.