In this paper we consider two non-independent random vectors XpXianiVqxlhaving multivariate normal distribution and obtain the maximum likelihood and the minimum variance unbiased estimates of R=Pr (a′x>b′y)where a and b are two known vectors, The problem arises for example, in a system where the energy is supplied to the system by p sources and is consumed through q sources. Some interesting special cases are deduced. A simulation study was carried out to compare the MVUE and MLE of B.An application is provided to determine the effect of a certain drug on the level of biochemical compounds found in the brain.