2025 Cayley Problem 13

Farhan has a blue hat, a white hat, a blue scarf, a white scarf, and a green scarf. He randomly chooses one hat and one scarf. What is the probability that the hat and the scarf are the same colour?

\textbf{(A)}\ \frac{1}{3}\quad \textbf{(B)}\ \frac{2}{5}\quad \textbf{(C)}\ \frac{2}{3}\quad \textbf{(D)}\ \frac{3}{5}\quad \textbf{(E)}\ \frac{1}{6}

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 Cayley contests here.