In most demographic studies censoring may occur. If that happens, analysis based on complete samples would not yield accurate estimates of vital Demographic estimates. In this paper we introduce a method for estimating the probability of occurrence of an event subject to censoring. We treat the problem under the assumption that the time to event during the enrollment time is an exponential distribution with two parameters. The censoring distribution during the follow-up period is taken to be uniform in each case. An application to infant mortality data extracted from PAPCHILD (1991) is presented.