# Random Answer, Correct! - Part 2

John has just registered an account on Brilliant. Each day, starting from today, he logs in, chooses a multiple choice problem, randomly answers it, and logs out. So if he is incorrect on one day, he loses his problem solving streak.

He stops this procedure once he gets a problem incorrect, or once he gets a streak of 10 days. The expected length of John's streak can be written as $$\frac{p}{q}$$, where $$p$$ and $$q$$ are coprime. Find the last $$3$$ digits of $$p+q$$.

Note: The streak can be 0, in case that John gets the problem he answers on the first day incorrect.

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