Inspired by Azhaghu Roopesh - A Valentine's Day Problem
On Valentine's day as usually happens , there was a girl who had recieved 2 proposals . The boys who had proposed to her were @Pratik Shastri and @Vraj Mehta . The girl however liked both of them , so she was in a fix .
However I knew that both were Scholars so I asked her conduct a test to decide who would get to be her boy friend .
Given below is her test :
" A given line segment is divided at \(3\) random into parts . What is the probability for the existence of a triangle whose medians are the three parts of the segment ? "
Eventually one of them did go on to solve the question correctly and win the heart of his Lady Love .
Your question : What is the correct answer as answered by the Lucky Boy ?
Kudos to those who can guess who won the girl's heart .