An experiment measures events containing a pair of particles reconstructed as electrons. The collected data sample, denoted by PP, is affected by two sources of background: the first consists of one real electron and one pion misidentified as an electron; the second consists of two mis-identified pions. The pion mis-identification probability f1,2i for both reconstructed objects and for each event i is known from simulation. Two independent data samples, containing, respectively, exactly one (PF) and exactly zero (FF) reconstructed electrons are also measured. Assume a perfect identification probability for real electrons. Estimate the total background yield in the PP sample.