In the above cases of two categories (binomial logistic regression), the categories were indexed by "0" and "1", and we had two probability distributions: The probability that the outcome was in category 1 was given by p(\boldsymbol{x})and the probability that the outcome was in category 0 was given by 1-p(\boldsymbol{x}). The sum of both probabilities is equal to unity, as they must be.
