One third of the buses from City A to City B stop at City C, while the rest go non-stop to City B. One third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C. All the buses have equal capacity and always start full from City A. What proportion of the passengers going to City B from City A travel by a bus stopping at City C?

A

$$\frac{1}{7}$$

B

$$\frac{1}{9}$$

C

$$\frac{1}{3}$$

D

$$\frac{7}{9}$$

E

$$\frac{4}{9}$$