The diluted mixed spin Ising system consisting of spin-1/2 and spin- I with a transverse random field is studied by the use of an effective field method within the framework of a single-site cluster theory. The equations are derived using a probability distribution method based on the use of Van der Waerden identities. The phase diagrams are investigated for various lattice structures both for pure and diluted systems, where the transverse field is bimodally and trimodally distributed.