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A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are shorter than $2$ units?

Jul 27, 2021

#1
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Use geometric probability! We are choosing random $x,y,z\ge 0$ such that $x+y+z=5$. We want the probability that $x,y,z\le 2$. The first equation is a plane, the second is a cube. Using the lower bounds on x,y,z, we get a pyramid. The volume of the pyramid is $\frac{125}{6}$. Therefore, the answer is

$$\frac{8}{\frac{125}{6}}=\frac{48}{125}$$

Jul 27, 2021
edited by thedudemanguyperson  Jul 27, 2021
#2
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Sorry but that is wrong

Guest Jul 27, 2021
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Are you sure the question is correct? I have found multiple questions identical to this one just asking for all the pieces greater than $1$.

thedudemanguyperson  Jul 27, 2021
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The questions asking for greater than 1 are different from this question

Guest Jul 27, 2021