Problem:
Let be the set of sides and diagonals of a regular pentagon. A pair of elements of are selected at random without replacement. What is the probability that the two chosen segments have the same length?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The five sides of the pentagon are congruent, and the five congruent diagonals are longer than the sides. Once one segment is selected, of the remaining segments have the same length as that segment. Therefore the requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions