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Text Solution:

Let’s define A as chocolate is dark and B as chocolate is round. Using the above formula, we have:

$\Rightarrow$ P(A) = $\frac{8}{15}$

$\Rightarrow$ P(B) = $\frac{9}{20}$

We are told that the probability of selecting a round and dark chocolate candy is $\frac{1}{5}$:

$\Rightarrow$ P(both A and B) = $\frac{1}{5}$

$\Rightarrow$ 1 = P(A) + P(B) - P(both A and B) + P(neither A nor B)

$\Rightarrow$ 1 = $\frac{8}{15}+\frac{9}{20}-\frac{1}{5}+P\left(\text{neither A nor B}\right)$

$\Rightarrow$ 1 = $\frac{32}{60}+\frac{27}{60}-\frac{12}{60}+P\left(\text{neither A nor B}\right)$  

$\Rightarrow$ 1 = $\frac{47}{60}+P\left(\text{neither A nor B}\right)$

Therefore, the probability that a randomly selected chocolate is neither dark nor round is $1-\frac{47}{60}=\frac{13}{60}$.