We give an elementary proof of the Pieri-type formula in the cohomology
of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or
symplectic vector space. This proof proceeds by explicitly computing a
triple intersection of Schubert varieties. The decisive step is an explicit
description of the intersection of two Schubert varieties, from which the
multiplicities (powers of 2) in the Pieri-type formula are
deduced.