  Given an element in a finite-dimensional real vector space, $V$, that is a
nonnegative linear combination of basis vectors for some basis $B$, we compute
the probability that it is furthermore a nonnegative linear combination of
basis vectors for a second basis, $A$. We then apply this general result to
combinatorially compute the probability that a symmetric function is
Schur-positive (recovering the recent result of Bergeron--Patrias--Reiner),
$e$-positive or $h$-positive. Similarly we compute the probability that a
quasisymmetric function is quasisymmetric Schur-positive or
fundamental-positive. In every case we conclude that the probability tends to
zero as the degree of a function tends to infinity.
