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?
+605 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
$$\frac{8}{\frac{125}{6}}=\frac{48}{125}$$
+605 Are you sure the question is correct? I have found multiple questions identical to this one just asking for all the pieces greater than $1$.
