MathDB

2

Part of 2021 IMC

Problems(1)

IMC 2021, first day , problem 2

Source: IMC , first day , problem 2

8/4/2021
Let nn and kk be fixed positive integers , and aa be arbitrary nonnegative integer . Choose a random kk-element subset XX of {1,2,...,k+a}\{1,2,...,k+a\} uniformly (i.e., all k-element subsets are chosen with the same probability) and, independently of XX, choose random n-elements subset YY of {1,2,..,k+a+n}\{1,2,..,k+a+n\} uniformly. Prove that the probability P(min(Y)>max(X))P\left( \text{min}(Y)>\text{max}(X)\right) does not depend on aa.
probabilityprobability and statsIMC 2021