Problem:
A set of three points is chosen randomly from the grid shown. Each three-point set has the same probability of being chosen. What is the probability that the points lie on the same straight line?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The number of three-point sets that can be chosen from the nine grid points is
Eight of these sets consist of three collinear points:
sets of points lie on vertical lines, on horizontal lines, and on diagonals. Hence the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions