In a city where all streets run east-to-west, all avenues run north-to-south…

In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles as shown below, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?

This problem refers to a figure in its source book that isn't reproduced here.

AQuA-RAT — Algebra Question Answering with Rationales (Ling et al., DeepMind, 2017) · train #45346