This work is concerned with two Bayesian predication problems if the sample size of the future sample is a random variable and samples are drawn from one parameter exponential. The first one is the predictive distribution of the difference (X_(s)-X_(r)) and the second is the prediction of the future sth order statistics. All the corresponding earlier results which depend on fixed sample size may be considered as special cases, very recent results derived by Lingappaiah (1986) may be considered as a special case from the present results. A numerical illustration is carried out to illustrate the new results.