The effects of crystal field (Delta) which is randomly turned on with probability p or turned off with probability 1-p on the sites of the Bethe lattice are investigated to study the critical behavior of the spin-3/2 Blume-Capel model. The order-parameters are obtained in terms of the recursion relations and then the possible phase diagrams are calculated at finite temperatures for given system parameters p, Delta and coordination numbers z=3, 4, 5 and 6. It was found that the phase diagrams change drastically for given probability and randomness. The first-order phase transitions are only found for higher p values and the lines of which get shorter and eventually disappearas p decreases. The critical lines do not present any qualitative differences with z, but they are seen at higher temperatures for higher z. (C) 2011 Elsevier B.V. All rights reserved.