2025 AMC 10A Problem 16

There are three jars. Each of three coins is placed in one of the three jars, chosen at random and independently of the placements of the other coins. What is the expected number of coins in a jar with the most coins?

\textbf{(A)} \dfrac{4}{3} \qquad \textbf{(B)} \dfrac{39}{27} \qquad \textbf{(C)} \dfrac{5}{3} \qquad \textbf{(D)} \dfrac{17}{9} \qquad \textbf{(E)} 2

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