MathDB

Let

R

be the rectangle in the Cartesian plane with vertices at

(0,0)

(2,0)

(2,1)

, and

(0,1)

R

can be divided into two unit squares, as shown. [asy]size(120); defaultpen(linewidth(0.7)); draw(origin--(2,0)--(2,1)--(0,1)--cycle^^(1,0)--(1,1));[/asy] Pro selects a point

P

at random in the interior of

R

. Find the probability that the line through

P

with slope

\frac{1}{2}

will pass through both unit squares.

Problem Statement