  We focus on checking the validity of the half-plane property on two prominent
classes of transversal matroids, namely lattice path matroids and bicircular
matroids. We show that lattice path matroids satisfy the half-plane property.
Subsequently, we show an explicit example of a bicircular matroid that is not a
positroid and discuss the negative correlation properties of bases of
transversal matroids. We prove that sparse paving matroids do not satisfy the
Rayleigh property, which helps us gain new perspectives about conjectures on
negative correlation in basis elements of matroids in general.
