MathDB

Parallel lines

\ell_1

\ell_2

\ell_3

\ell_4

are evenly spaced in the plane, in that order. Square

ABCD

has the property that

A

lies on

\ell_1

and

C

lies on

\ell_4

. Let

P

be a uniformly random point in the interior of

ABCD

and let

Q

be a uniformly random point on the perimeter of

ABCD

. Given that the probability that

P

lies between

\ell_2

and

\ell_3

\frac{53}{100}

, the probability that

Q

lies between

\ell_2

and

\ell_3

can be expressed as

\frac{a}{b}

, where

a

and

b

are relatively prime positive integers. Compute

100a + b

Problem Statement