  We present in this paper an approximation that is able to give an analytical
expression for the exit probability of the $q$-voter model in one dimension.
This expression gives a better fit for the more recent data about simulations
in large networks, and as such, departs from the expression
$\frac{\rho^q}{\rho^q + (1-\rho)^q}$ found in papers that investigated small
networks only. The approximation consists in assuming a large separation on the
time scales at which active groups of agents convince inactive ones and the
time taken in the competition between active groups. Some interesting findings
are that for $q=2$ we still have $\frac{\rho^2}{\rho^2 + (1-\rho)^2}$ as the
exit probability and for large values of $q$ the difference between the result
and $\frac{\rho^q}{\rho^q + (1-\rho)^q}$ becomes negligible (the difference is
maximum for $q=5$ and 6)
