# Two Random Walks

Bug $$A$$ starts on the origin on the coordinate plane and makes $$3$$ random unit moves only in the four compass directions (Up, Down, Left, Right). Bug $$B$$ starts on coordinate $$(1,0)$$ and makes two random unit moves only in the four compass directions. The probability that bug $$B$$ is closer or equal in distance to the origin with bug $$A$$ can be expressed as $$\dfrac{p}{q}$$ for positive coprime integers $$p,q.$$ Find $$p+q$$.

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