## Elementary Statistics (12th Edition)

$0.25$
It is possible to solve this problem using Maths, butwe can also solve this problem qualitatively. If we want a shape to be a triangle, two of the sides formed must add up to be greater than the length of the longest side (Triangle-inequality). Because there are infinite points on a line, the odds are effectively $100\%=1$ that the first point chosen will not be in the middle of the rod. This point effectively breaks the rod into two pieces of different sizes. If the point chosen happens to be on the shorter piece, the triangle cannot be formed, and if the point chosen is on the longer piece in a location that makes it so that the two shortest sides formed are less than or equal to the length of the longest side, the triangle will not be formed. Hence we can see that there are four possibilities, and only one allows a triangle to be formed. Therefore the probability is $\frac{1}{4}=0.25$.