Parity of coefficients of mock theta functions

We study the parity of coefficients of classical mock theta functions. Let $c(g;n)$ be the coefficient of $q^n$ in the series expansion of $g(q)$. For a power series $g(q)$ with integer coefficients, we say that $g$ is of type $(a,1-a)$ modulo 2 if $c(g;n)$ takes even values with probability $a$. We show that among the 44 classical mock theta functions, 21 of them are of type $(1,0)$ modulo 2. We further conjecture that 19 mock theta functions are of type $(\frac{1}{2},\frac{1}{2})$ and 4 functions are of type $(\frac{3}{4},\frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of type $(1,0)$.