The location of trees in an even, rectangular forest stand of size \(200 \mathrm{~m} \times 500 \mathrm{~m}\) follows a homogeneous Poisson distribution with intensity \(\lambda=1\) per \(25 \mathrm{~m}^{2}\). The diameters of the stems of all trees at a distance of \(130 \mathrm{~cm}\) to the ground is assumed to be \(24 \mathrm{~cm}\). From outside, a shot is vertically fired at a \(500 \mathrm{~m}\) side of the forest stand (parallel to the ground at level \(130 \mathrm{~cm}\) ). What is the probability that a bullet with diameter \(1 \mathrm{~cm}\) hits no tree?

With regard to the question, the location of a tree is fully determined by the coordinates of the center of the cross-section of its stem at level \(130 \mathrm{~cm}\).