MathDB
Probabilty

Source: IMS 2008

May 10, 2008
probabilityprobability and stats

Problem Statement

In a contest there are n n yes-no problems. We know that no two contestants have the same set of answers. To each question we give a random uniform grade of set {1,2,3,,2n} \{1,2,3,\dots,2n\}. Prove that the probability that exactly one person gets first is at least 12 \frac12.