Breaking The Rod!!

A wooden rod is 6 m long. 2 points A and B on the rod are uniformly and independently chosen. The rod is then cut at both points to obtain a smaller rod AB.

Find the chance that the rod AB will be at least 1m in length. If the chance can be written as \( \frac{a}{b} \), where \(a, b \) are positive coprime integers, find \( a + b \).

Image credit: Adapated from Wikipedia ArnoldReinhold.

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