TxO Math Bowl 2024 - Team Contest - Problem 8

Consider the open interval from 0 to 5 on a number line. Two distinct points x and y are chosen at random on the open interval with no restrictions. These points divide the number line into 3 regions a, b, and c from left to right. The probability that a < 2b < c can be expressed as \frac{m}{n}, where m and n are relatively prime, positive integers. Compute the value of m + n.