Passing Through B

Difficulty: Medium · Topics: Probability, Probability, Combinations

A walker starts at A and, moving only right or down along the grid, goes to C, choosing one of the shortest routes at random.

graph "x":[-0.7,6.7],"y":[-0.7,4.7],"axes":false,"ink":true,"label":"A 6 by 4 street grid from A (top left) to C (bottom right) with point B","items":["type":"line","from":[0,0],"to":[6,0],"ink":true,"width":1.2,"type":"line","from":[0,1],"to":[6,1],"ink":true,"width":1.2,"type":"line","from":[0,2],"to":[6,2],"ink":true,"width":1.2,"type":"line","from":[0,3],"to":[6,3],"ink":true,"width":1.2,"type":"line","from":[0,4],"to":[6,4],"ink":true,"width":1.2,"type":"line","from":[0,0],"to":[0,4],"ink":true,"width":1.2,"type":"line","from":[1,0],"to":[1,4],"ink":true,"width":1.2,"type":"line","from":[2,0],"to":[2,4],"ink":true,"width":1.2,"type":"line","from":[3,0],"to":[3,4],"ink":true,"width":1.2,"type":"line","from":[4,0],"to":[4,4],"ink":true,"width":1.2,"type":"line","from":[5,0],"to":[5,4],"ink":true,"width":1.2,"type":"line","from":[6,0],"to":[6,4],"ink":true,"width":1.2,"type":"point","at":[0,4],"label":"A","anchor":"nw","ink":true,"type":"point","at":[2,2],"label":"B","anchor":"nw","ink":true,"type":"point","at":[6,0],"label":"C","anchor":"se","ink":true]

What is the probability that the walker passes through B?