  We introduce the notion of a probabilistic identity of a residually finite
group. We prove that a finitely generated linear group satisfies a
probabilistic identity if and only if it is virtually solvable.
  As an application, we prove a probabilistic variant of the Tits alternative:
let G be the profinite completion of a finitely generated linear group. Then
either G is virtually solvable, or for any positive integer n, with probability
one, n independent, uniformly distributed elements of G freely generate a free
subgroup of G of rank n.
