Triangle ABC is equilateral with side length 3. A point X is randomly chosen within ABC. What is the probability that X is no more than 1 unit away from vertex?
Point X must be in three small equilateral triangles, each with side length. Each small equilateral triangle has 1/9 the area of the large equilateral triangle, so the probability is 3/9 = 1/3.
+19 
