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?

The best solution was submitted by Huy Tùng Nguyễn (수리과학과 2016학번). Congratulations!

Here is his solution of problem 2017-22.

Alternative solutions were submitted by 최대범 (수리과학과 2016학번, +3), 김태균 (수리과학과 2016학번, +2), 유찬진 (수리과학과 2015학번, +2). One incorrect solution was received.

(This is the last problem of this semester. Thank you all for participating POW.)