-2
$\begingroup$

A stick is randomly broken into 3 pieces . Determine the probability that the sum of the lengths of any 2 pieces is greater than the length of the third piece.

$\endgroup$
  • $\begingroup$ As I understand the problem, the probability is 1, since you can choose the largest two pieces to begin with. $\endgroup$ – Marc Apr 12 '16 at 11:49
  • $\begingroup$ the question probably meant any random 2 pieces chosen $\endgroup$ – user330785 Apr 12 '16 at 11:51
  • 2
    $\begingroup$ This is a well known problem...you can read about the usual formulation here or for some variants here $\endgroup$ – lulu Apr 12 '16 at 11:55
0
$\begingroup$

Geometric solution (non-strict): let $x$, $y$ and $z$ be lengths of pieces. Then in space with $xyz$ axes you have a triangle ($x+y+z=L, x\ge 0, y\ge 0, z \ge 0$). Total area of triangle corresponds to probability 1. Subsets of fitting pieces also correspond to a triangle, with area $1/4$ of the original one.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.