Probability of X being greater than Y for independent uniform variables

[magnifik]

Let X and Y be independent and uniform on {1, 2, ... M}
Find P(X > Y)

so i know that P(X = x) = 1/M and P(Y = y) = 1/M
i don't understand how Find P(X > Y) = (M+1)/2M

 

[I like Serena]

Hi magnifik!

Suppose M=3.

Then we have the matrix:

X\Y   1  2  3
1     ≥
2     ≥  ≥
3     ≥  ≥  ≥

In how many cases is the condition satisfied?
And what is the total number of cases?