## Problem of the week

### 2017-22 Debugging

Let $$p$$, $$q$$, $$r$$ be positive integers such that $$p,q\ge r$$. Ada and Betty independently read all source codes of their programming project. Ada found $$p$$ bugs and Betty found $$q$$ bugs, including $$r$$ bugs that Ada found. What is the expected number of remaining bugs that neither Ada nor Betty found?