Difference between revisions of "2022 SSMO Relay Round 4 Problems/Problem 1"
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Latest revision as of 13:11, 14 December 2023
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