  We study the first-passage time to the origin of a mortal Brownian particle,
with mortality rate $ \mu $, diffusing in one dimension. The particle starts
its motion from $ x>0 $ and it is subject to stochastic resetting with constant
rate $ r $. We first unveil the relation between the probability of reaching
the target and the mean first-passage time of the corresponding problem in
absence of mortality, which allows us to deduce under which conditions the
former can be increased by adjusting the restart rate. We then consider the
first-passage time conditioned on the event that the particle reaches the
target before dying, and provide exact expressions for the mean and the
variance as functions of $ r $, corroborated by numerical simulations. By
studying the impact of resetting for different mortality regimes, we also show
that, if the average lifetime $ \tau_\mu=1/\mu $ is long enough with respect to
the diffusive time scale $ \tau_D=x^2/(4D) $, there exist both a resetting rate
$ r_\mu^* $ that maximizes the probability and a rate $ r_m $ that minimizes
the mean first-passage time. However, the two never coincide for positive $ \mu
$, making the optimization problem highly nontrivial.
