2024 SSMO Relay Round 5 Problems/Problem 2

Problem

Let In the game of high and low, the computer chooses two integers without replacement from the set . The computer displays the first integer and asks the player if the second integer is higher or lower. Given that the player always plays optimally, the chances of guessing correctly is for relatively prime positive integers and Find

Solution

Note that if the computer chooses then there is a chance that the player guesses correctly and if then there is a chance that the player guesses correctly. Thus, the answer is

~SMO_Team