A draws a card from a pack of n cards marked 1,2,……..n. The card is replaced in the pack and B draws a card.  Then the probability that A draws a higher card than B is

If A draws card higher than B, then the number of favorable cases is  (n−1)+(n−2)+⋯+3+2+1 (as when B draws card number 1, then A can draw any card from 2 to n and so on). Therefore, the required probability is n(n−1)2n2=n−12n