MathDB

Let

C

be the unit circle

x^{2}+y^{2}=1 .

A point

p

is chosen randomly on the circumference

C

and another point

q

is chosen randomly from the interior of

C

(these points are chosen independently and uniformly over their domains). Let

R

be the rectangle with sides parallel to the

x

and

y

-axes with diagonal

p q .

What is the probability that no point of

R

lies outside of

C ?

B4