# Question about three Normal distributions

Let there be 3 normal distributions $X\sim\mathcal{N}(\mu_x,\sigma_x)$, $Y\sim\mathcal{N}(\mu_y,\sigma_y)$, $Z\sim\mathcal{N}(\mu_z,\sigma_z)$ and 3 random samples from each distribution- $x,y,z$. how can I find the probability of $P(x>y\textrm{ and } x>z)$. That is, the probability that the sample $x$ will be larger both from the sample $y$ and from the sample $z$. (assuming the distributions are independent)

Thanks for the help!