  We study active particles performing independent run and tumble motion on an
infinite line with velocities $v_0 \sigma(t)$, where $\sigma(t) = \pm 1$ is a
dichotomous telegraphic noise with constant flipping rate $\gamma$. We first
consider one particle in the presence of an absorbing wall at $x=0$ and
calculate the probability that it has survived up to time $t$ and is at
position $x$ at time $t$. We then consider two particles with independent
telegraphic noises and compute exactly the probability that they do not cross
up to time $t$. Contrarily to the case of passive (Brownian) particles this
two-RTP problem can not be reduced to a single RTP with an absorbing wall.
Nevertheless, we are able to compute exactly the probability of no-crossing of
two independent RTP's up to time $t$ and find that it decays at large time as
$t^{-1/2}$ with an amplitude that depends on the initial condition. The latter
allows to define an effective length scale, analogous to the so called `` Milne
extrapolation length'' in neutron scattering, which we demonstrate to be a
fingerprint of the active dynamics.
