Empty red-red-blue triangles

Let $P$ be a $2n$-point set in the plane that is in general position. We prove that every red-blue bipartition of $P$ into $R$ and $B$ with $\mathrm{\mid }R\mathrm{\mid }=\mathrm{\mid }B\mathrm{\mid }=n$ generates $\mathrm{\Omega }(n^{3\mathrm{/}2})$ red-red-blue empty triangles.