NeuroEducation

A Vertex at the Crossing

Difficulty: Medium · Topics: Probability, Probability, Combinations

Points A, B, C lie on line d 1 and points A, D, E, F lie on line d 2.

graph "x":[-0.8,6.0],"y":[-1.6,2.2],"axes":false,"ink":true,"label":"Two lines meeting at A: d1 also passes through B and C, d2 through D, E and F","items":["type":"line","from":[0,-0.35],"to":[5.2,1.6],"type":"line","from":[0,0.9],"to":[5.2,-1.3],"type":"label","at":[5.55,1.75],"text":"d₁","type":"label","at":[5.55,-1.45],"text":"d₂","type":"point","at":[1.566,0.237],"label":"A","anchor":"n","type":"point","at":[3.0,0.775],"label":"B","anchor":"n","type":"point","at":[3.9,1.1124999999999998],"label":"C","anchor":"n","type":"point","at":[2.9,-0.32692307692307676],"label":"D","anchor":"s","type":"point","at":[3.7,-0.6653846153846154],"label":"E","anchor":"s","type":"point","at":[4.5,-1.0038461538461538],"label":"F","anchor":"s"]

One of the triangles formed by these points is chosen at random. What is the probability that A is one of its vertices?