  We consider search by mobile agents for a hidden, idle target, placed on the
infinite line. Feasible solutions are agent trajectories in which all agents
reach the target sooner or later. A special feature of our problem is that the
agents are $p$-faulty, meaning that every attempt to change direction is an
independent Bernoulli trial with known probability $p$, where $p$ is the
probability that a turn fails. We are looking for agent trajectories that
minimize the worst-case expected termination time, relative to competitive
analysis.
  First, we study linear search with one deterministic $p$-faulty agent, i.e.,
with no access to random oracles, $p\in (0,1/2)$. For this problem, we provide
trajectories that leverage the probabilistic faults into an algorithmic
advantage. Our strongest result pertains to a search algorithm (deterministic,
aside from the adversarial probabilistic faults) which, as $p\to 0$, has
optimal performance $4.59112+\epsilon$, up to the additive term $\epsilon$ that
can be arbitrarily small. Additionally, it has performance less than $9$ for
$p\leq 0.390388$. When $p\to 1/2$, our algorithm has performance
$\Theta(1/(1-2p))$, which we also show is optimal up to a constant factor.
  Second, we consider linear search with two $p$-faulty agents, $p\in (0,1/2)$,
for which we provide three algorithms of different advantages, all with a
bounded competitive ratio even as $p\rightarrow 1/2$. Indeed, for this problem,
we show how the agents can simulate the trajectory of any $0$-faulty agent
(deterministic or randomized), independently of the underlying communication
model. As a result, searching with two agents allows for a solution with a
competitive ratio of $9+\epsilon$, or a competitive ratio of
$4.59112+\epsilon$. Our final contribution is a novel algorithm for searching
with two $p$-faulty agents that achieves a competitive ratio
$3+4\sqrt{p(1-p)}$.
