The probability of triviality (Q1966131)

The following problems are treated: Given a variety \(V\) of type \(\tau \) and an identity \(p\approx q\) of type \(\tau \). What is the probability that \(p\approx q\) is satisfied only by the trivial algebra of \(V\)? If \(W\) is a subvariety of \(V\), what is the probability that \(p\approx q\) together with \(\text{Id}(V)\) form an equational basis for \(W\)? Some criteria that allow explicit calculation of these probabilities are presented.