A binary Markov process model is proposed for the random testing of software. This model is suggested for replacing the standard binomial distribution model, which is based on the easily-violated assumption of test runs being statistically independent of each other. In addition to a general result on the probability of having any specific number of software failures during testing, practical implications of the new model are also discussed. In particular, we demonstrate that, in general, the effect of a possible correlation between test runs cannot be ignored in estimating software reliability.