The lines are infinitely thin. Equivalently you can imagine the paper is divided into regions of width L, and the question is whether the needle will cross a region boundary (<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Buffon&#x27;s_needle" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Buffon&#x27;s_needle</a>).