  In a wide range of complex networks, the links between the nodes are temporal
and may sporadically appear and disappear. This temporality is fundamental to
analyze the formation of paths within such networks. Moreover, the presence of
the links between the nodes is a random process induced by nature in many
real-world networks. In this paper, we study random temporal networks at a
microscopic level and formulate the \emph{probability of accessibility} from a
node \emph{i} to a node \emph{j} after a certain number of discrete time units
$T$. While solving the original problem is computationally intractable, we
provide an upper and two lower bounds on this probability for a very general
case with arbitrary time-varying probabilities of links' existence. Moreover,
for a special case where the links have identical probabilities across the
network at each time slot, we obtain the exact probability of accessibility
between any two nodes. Finally, we discuss scenarios where the information
regarding the presence and absence of links is initially available in the form
of time duration (of presence or absence intervals) continuous probability
distributions rather than discrete probabilities over time slots. We provide a
method for transforming such distributions to discrete probabilities which
enables us to apply the given bounds in this paper to a broader range of
problem settings.
