Why is the oxygen saturation curve of haemoglobin sigmoidal?

The saturation curve of haemoglobin shows positive cooperativity. Initially, the porphyrin ring of the haem prosthetic group in haemoglobin is dome-shaped. When one molecule of oxygen binds one of the four sites of oxygen binding, it pulls the iron ion in the porphyrin ring into the plane of the ring. The haemoglobin tetramer undergoes a conformational change that is transmitted to all of its subunits, causing them to shift from the tense state to the relaxed state, making another molecule of oxygen more likely to bind. The saturation begins to plateau at very high partial pressures of oxygen because the sheer probability of a single haemoglobin tetramer encountering four independent oxygen molecules in the correct orientation is low.