  In this paper, we prove a new expected dimension formula for certain rank two
Brill-Noether loci with fixed special determinant. This answers a question
asked by Osserman and also leads to a new and much simpler proof of a theorem
of Osserman. Our result generalizes the well-known result by Bertram, Feinberg
and independently Mukai on expected dimension of rank two Brill-Noether loci
with canonical determinant and partially verifies a conjecture (in rank two) of
Grzegorczyk and Newstead on coherent systems.
