Let two random vectors $X_1$ and $X_2$ be jointly distributed as a normal distribution with mean $\mu$ and covariance matrix $\sum_1$. Let $\Pi (\lambda)$be the probability that $X_1\in C_1, X_2\in C_2$, where $C_1$ and $C_2$ are convex symmetric sets, when the covariance matrix between $X_1$ and $X_2$ is multiplied by $\lambda;0\leq \lambda \leq 1$. It is shown that $\Pi(\lambda)$ increases with $\lambda$ under some conditions on $\mu$ and $\sum_1$. This generalizes the results of Das Gupta et al (1972), Khatri (1967) and Šidák (1973).
 Das Gupta S., Eaton M. L., Olkin I., Perlman M. D., Savage L. J., and Sobel M.: Inequalities on the probability content of convex regions for elliptically contoured distributions
. Proc. Sixth Berk. Symp. on Math. Stat. and Prob. Vol. 11, (1972), 241-265. MR 0413364
 Šidák Z.: On probabilities in certain multivariate distributions: their dependence on correlations
. Aplikace Matematiky 18, (1973), 128-135. MR 0314197