  We use the Chebyshev knot diagram model of Koseleff and Pecker in order to
introduce a random knot diagram model by assigning the crossings to be positive
or negative uniformly at random. We give a formula for the probability of
choosing a knot at random among all knots with bridge index at most 2.
Restricted to this class, we define internal and external reduction moves that
decrease the number of crossings of the diagram. We make calculations based on
our formula, showing the numerics in graphs and providing evidence for our
conjecture that the probability of any knot appearing in this model decays to
zero as the number of crossings goes to infinity.
