ANOTHER probability, plz help??

Question

On each tile in a set of dominoes, each integer 0 through 14 is paired exactly once with each integer 0 through 14 . One number of the pair is written on one half of the domino, and the other number is written on the other half. If one domino is selected at random from all the dominoes in this set, what is the probability that the same number will be on both halves? Express your answer as a common fraction in lowest terms.

The right answer is 1/8 , plz show steps and best answer will be given

Answer 1

So our numbers,  (x,y) should meet the conditions such that:

x ≤ y and 0 ≤ x ≤  n-1 and 0 ≤ y ≤ n-1

We have (n² -n)/2 + n of them and n couples are of the form (x,x). Hence the answer is

n /( (n² -n)/2 + n)=2/(n+1). In our case, n=14+1=15.

So the answer is 2/(15 +1) = 2/16

= 1/8 <~~Answer