Two integers x and y are chosen with replacement out of the set (0, 1, 2, 3,..., 10). Then the probability that |x - y| >5, is

$\frac{30}{121}$

Since x and y each can take values from 0 to 10. So, the total number of ways of selecting x and y is 11 × 11 =121. 

Now,$| x-y|>5⇒x-y<-5$ or,$ x-y>5$

There are 30 pairs of values of x and y satisfying these two inequalities.

So, favourable number of elementary events = 30.

Hence, required probability $=\frac{30}{121}$