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\binom{4}{2} \left(\frac{1}{3}\right)^2 \left(\frac{2}{3}\right)^2 = 6 \cdot \frac{1}{9} \cdot \frac{4}{9} = \frac{24}{81} = \frac{8}{27}.
The probability is $\boxed{\dfrac{8}{27}}$.
Question: A neural interface system processes 5 distinct signals using 3 unique channels. How many ways can the signals be assigned to channels if each channel can process any number of signals?

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