Question 45
If we pick (uniformly) a random square of area $1$ with sides parallel to the $x$- and $y$-axes that lies entirely within the $5$-by-$5$ square bounded by the lines $x=0$, $x=5$, $y=0$, $y=5$ (the corners of the square need not have integer coordinates), what is the probability that the point $(x, y) = (4.5, 0.5)$ lies within the square of area $1$?