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# probability

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A line segment is broken at two random points along its length. What is the probability that the three new segments can be arranged to form a triangle?

Apr 1, 2021

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I like this one. Let the sides be $x,y,1-(x+y)$. By the triangle inequality, all of the following must be true:

$$x<1-x$$

$$y<1-y$$

$$1<2x+2y$$

Graph each of these on the coordinate plane and use the principle of geometric probability. It's $\frac14$.

Apr 1, 2021