MathDB

Dave arrives at an airport which has twelve gates arranged in a straight line with exactly

100

feet between adjacent gates. His departure gate is assigned at random. After waiting at that gate, Dave is told the departure gate has been changed to a different gate, again at random. Let the probability that Dave walks

400

feet or less to the new gate be a fraction

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find m\plus{}n.

Problem Statement