$14 \cdot 8$ In a plane, any point chosen has rectangular coordinates that are integers with absolute values less than or equal to 4, and all such points are equally likely to be chosen. The probability that the distance from the chosen point to the origin is at most 2 units is
(A) $\frac{13}{81}$.
(B) $\frac{15}{81}$.
(C) $\frac{13}{64}$.
(D) $\frac{\pi}{16}$.
(E) the square of a rational number.
(27th American High School Mathematics Examination, 1976)
[Solution] The points whose coordinates are integers with absolute values less than or equal to 4 form a $9 \times 9$ array of points centered at the origin.
Among these points, 13 points are at a distance from the origin of less than or equal to 2 units.
Therefore, the required probability is $\frac{13}{81}$. Hence, the answer is $(A)$.