P(X=Y)=\sum_{k=1}^{n}P(X=k,Y=k)=nezavisnost=\sum_{k=1}^{n}P(X=k)P(Y=k)=\sum_{k=1}^{n}\frac{1}{{n}^{2}}=n*\frac{1}{{n}^{2}}=\frac{1}{n}