A packing of a collection of subintervals of [0, 1] is a
pairwise disjoint subcollection of the intervals; its wasted space is
the measure of the set of points not covered by the packing.
¶ Consider n random intervals, $I_1, \dots, I_n$, chosen by
selecting endpoints independently from the uniform distribution. We strengthen
and simplify the results of Coffman, Poonen and Winkler, and we show that, for
some universal constant K and for each $t \geq 1$, with probability
greater than or equal to $1 - 1/n_t$, there is a packing with wasted space less
than or equal to $Kt (\log n)^2 /n$.