# Random Answer, Correct! - Part 2

**Discrete Mathematics**Level 5

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.