sat-dog

The correct answer is $\frac{1}{14}$. If one vertex of the polygon is selected at random, the probability that the letter $D$ will be at the selected vertex is equal to the number of vertices labeled with the letter $D$ divided by the total number of vertices. It's given that each vertex is labeled with one of the $14$ letters $A$ through $N$, with a different letter at each vertex. It follows that there is $1$ vertex labeled with the letter $D$. It's also given that the polygon is $14$-sided. It follows that there are a total of $14$ vertices. Thus, the probability that the letter $D$ will be at the selected vertex is $\frac{1}{14}$. Note that 1/14, .0714, and 0.071 are examples of ways to enter a correct answer.