Answer to Question #381 in Statistics and Probability for giselle
Now remember geometry. We can form a triangle with the three segments if and only if the length of each segment is less than the sum of the lengths of the other two segments. This condition in our case leads to a system of three inequalities:
x < y-x+l-y
l-y < x+y-x
y-x < x+l-y
The first inequality is transformed to the form x<(L/2), the second - to the form y>(L/2), and the third inequality – to the form y<(L/2). The set of pairs of numbers x and y is a solution of inequalities shown in the shaded triangle. The area of this triangle is 4 times smaller than the area of a triangle OBC. Thus, the answer is 1/4.
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