  We study a simple model of a diffusing particle (the prey) that on encounter
with one of a swarm of diffusing predators can either perish or be reset to its
original position at the origin. We show that the survival probability of the
prey up to time $t$ decays algebraically as $\sim t^{-\theta(p, \gamma)}$ where
the exponent $\theta$ depends continuously on two parameters of the model, with
$p$ denoting the probability that a prey survives upon encounter with a
predator and $\gamma = D_A/(D_A+D_B)$ where $D_A$ and $D_B$ are the diffusion
constants of the prey and the predator respectively. We also compute exactly
the probability distribution $P(N|t_c)$ of the total number of encounters till
the capture time $t_c$ and show that it exhibits an anomalous large deviation
form $P(N|t_c)\sim t_c^{- \Phi\left(\frac{N}{\ln t_c}=z\right)}$ for large
$t_c$. The rate function $\Phi(z)$ is computed explicitly. Numerical
simulations are in excellent agreement with our analytical results.
