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?

Question

merchandize · Answer

The indicated probability as an irreducible fraction is 1/6, therefore the answer is 1 + 6 = 7
Without loss of generality, we can assume that each toothpick is of length 1.
The two toothpick drops can be considered independently.
Let y be the length of the shorter piece in toothpick #1 and z be the length of the shorter piece in toothpick #2. It's obvious that 0