Each of 2023 balls is randomly placed into one of 3 bins. Which of the following is closest to the probability that each of the bins will contain an odd number of balls?

**Answer Choices**

A. \dfrac{2}{3}

B. \dfrac{3}{10}

C. \dfrac{1}{2}

D. \dfrac{1}{3}

E. \dfrac{1}{4}