Sobhan's Toothpick Sum

[protik]

Sobhan has two toothpicks each with the same length. 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 a/b where a and b are coprime positive integers. What is the value of a+b?

[sowmitra]

Courtesy: http://www.brilliant.org
Week of Jan-8.