# Sobhan's Toothpick Sum

**Discrete Mathematics**Level 4

Sobhan has two toothpicks with equal lengths. He accidentally drops the toothpicks to the floor and each one breaks into two pieces. The probability that the two largest pieces are each larger than the sum of the lengths of the the two smallest pieces can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are coprime positive integers. What is the value of \(a + b\)?

**Details and assumptions**

The (single) break in the toothpick occurs uniformly along its length.