Chebyshev’s inequality is a powerful probabilistic inequality based on which we can set up confidence interval of any random variable irrespective of its distribution. In the present paper, we make use of this inequality to set up confidence (fiducial) limits of a second and third order random determinant whose entries are independently and identically distributed Beta variates of first kind. The results would be useful in computations involving determinants where the entries are random variables and in areas where we are dealing with random square matrices.