2026 AMC 8 Problem 21

Charlotte the spider is walking along a web shaped like a 5-pointed star, shown in the figure below. The web has 5 outer points and 5 inner points. Each time Charlotte reaches a point, she randomly chooses a neighboring point and moves to that point. Charlotte starts at one of the outer points and makes 3 moves (re-visiting points is allowed). What is the probability she is now at one of the outer points of the star?

\textbf{(A)} \dfrac{1}{5} \qquad \textbf{(B)} \dfrac{1}{4} \qquad \textbf{(C)} \dfrac{2}{5} \qquad \textbf{(D)} \dfrac{1}{2} \qquad \textbf{(E)} \dfrac{3}{5}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.