2019 Gauss 8 Problem 15

A spinner is divided into 3 equal sections, as shown. An arrow is attached to the centre of the spinner. The arrow is spun twice. What is the probability that the arrow lands on the same colour twice?

\textbf{(A)}\ \frac{1}{9}\quad \textbf{(B)}\ \frac{2}{3}\quad \textbf{(C)}\ \frac{1}{2}\quad \textbf{(D)}\ \frac{1}{3}\quad \textbf{(E)}\ \frac{2}{9}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.