  We consider a random walk in a stationary ergodic environment in $\mathbb Z$,
with unbounded jumps. In addition to uniform ellipticity and a bound on the
tails of the possible jumps, we assume a condition of strong transience to the
right which implies that there are no "traps". We prove the law of large
numbers with positive speed, as well as the ergodicity of the environment seen
from the particle. Then, we consider Knudsen stochastic billiard with a drift
in a random tube in ${\mathbb R}^d$, $d\geq 3$, which serves as environment.
The tube is infinite in the first direction, and is a stationary and ergodic
process indexed by the first coordinate. A particle is moving in straight line
inside the tube, and has random bounces upon hitting the boundary, according to
the following modification of the cosine reflection law: the jumps in the
positive direction are always accepted while the jumps in the negative
direction may be rejected. Using the results for the random walk in random
environment together with an appropriate coupling, we deduce the law of large
numbers for the stochastic billiard with a drift.
