MathDB

Consider the L-shaped region formed by three unit squares joined at their sides, as shown below. Two points

A

and

B

are chosen independently and uniformly at random from inside this region. The probability that the midpoint of

\overline{AB}

also lies inside this L-shaped region can be expressed as

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n

. [asy] size(2.5cm); draw((0,0)--(0,2)--(1,2)--(1,1)--(2,1)--(2,0)--cycle); draw((0,1)--(1,1)--(1,0), dotted); [/asy]

Problem Statement