  Large-scale Monte Carlo simulations of the bond-diluted three-dimensional
4-state Potts model are performed. The phase diagram and the physical
properties at the phase transitions are studied using finite-size scaling
techniques. Evidences are given for the existence of a tricritical point
dividing the phase diagram into a regime where the transitions remain of first
order and a second regime where the transitions are softened to continuous ones
by the influence of disorder. In the former regime, the nature of the
transition is essentially clarified through an analysis of the energy
probability distribution. In the latter regime critical exponents are
estimated. Rare and typical events are identified and their role is
qualitatively discussed in both regimes.
