Let \(X\) be the height of the woman and \(Y\) be the height of the man in married couples in a certain geographical region. By analyzing a sufficiently large sample, a statistician found that the random vector \((X, Y)\) has a joint normal distribution with parameters

\[E(X)=168 \mathrm{~cm}, \operatorname{Var}(X)=64 \mathrm{~cm}^{2}, E(Y)=175 \mathrm{~cm}, \operatorname{Var}(Y)=100 \mathrm{~cm}^{2}, ho=0.86\]

(1) Determine the probability \(P(X>Y)\) that in married couples in this area a wife is taller than her spouse.

(2) Determine the same probability on condition that there is no correlation between \(X\) and \(Y\), and interprete the result in comparison to (1).