A box contains three red, three white, and three green balls. A ball is chosen at random. What is the probability that the ball picked up is neither white nor red?

In this question, we can first determine the total number of outcomes, the total number of favourable outcomes, and then, using the probability formula, we can determine the probability of receiving a ball that is neither red nor white. 

Now,

Total number of outcomes = total number of balls = 9

Number of favourable outcomes (the ball is neither white nor red) = 3

 $\therefore \mathrm{Required} \mathrm{probability}=\frac{\mathrm{number} \mathrm{of} \mathrm{favourable} \mathrm{outcomes}}{\mathrm{total} \mathrm{number} \mathrm{of} \mathrm{outcomes}}=\frac{3}{9}=\frac{1}{3}$

Hence, the correct answer is $\frac{1}{3}$.