  Iterated quadratic polynomials give rise to a rich collection of different
dynamical systems that are parametrized by a simple complex parameter $c$. The
different dynamical features are encoded by the \emph{kneading sequence} which
is an infinite sequence over $\{0,\1\}$. Not every such sequence actually
occurs in complex dynamics. The set of admissible kneading sequences was
described by Milnor and Thurston for real quadratic polynomials, and by the
authors in the complex case. We prove that the set of admissible kneading
sequences has positive Bernoulli measure within the set of sequences over
$\{0,\1\}$.
