Probability of selecting two numbers with a sum of squares divisible by 10 
Two natural numbers $x$ and $y$ are chosen at random.  Find the probability that $x^2 + y^2$ is divisible by 10.

I could not understand how select two numbers from any natural number (infinite). 

Its simple logic. Count numbers on the basis of last digits whose sum of square makes 0.
So Favourable cases = {(0,0),(1,3),(1,7),(2,4),(2,6),(3,1),(3,9),(4,2),(4,8),(5,5),(6,2),(6,8),(7,1),(7,9),(8,4)(8,6),(9,3),(9,7)} = 18
Total cases = Value of x can be any digit from 0 to 9. 
Similarly for y.
$= 10 * 10 = 100$
$Probability = \frac{\text{No. of favourable cases}}{\text{Total no. of cases}}$
$= \frac{18}{100} = \frac{9}{50} $
