Consider a pair of random variables X and Y, each of which t…

Consider a pair of random variables X and Y, each of which take on values on the set A={1,2,…,[n]}. The joint distribution of X and Y is a constant for all (x,y) pairs coming from the set A above. Let the random variable Z be given as the maximum of X and Y.  Find the probability that Z is less than or equal to [k].