  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 (which
are powers of 2) in the Pieri-type formula are deduced.
