2022 SSMO Relay Round 4 Problems/Problem 1
Problem
On any given day, there is a 
chance that a robot will find a new organism, a 
chance it will find an already discovered organism, and a 
chance that it will find nothing. Given that it has found a new organism, there is a 
chance it will correctly determine that it is a new organism, and given that it has found an already discovered organism, there is a 
chance that it will correctly determine that it has already been discovered. The expected number of days that the robot will take to report that it has found a new organism (regardless of whether it actually has) can be expressed as 
where 
and 
are relatively prime positive integers. Find 
