Cards numbered 1, 2, . . . , n are randomly distributed to players 1, 2, . . . , n. Whenever two players compare their numbers, the one with the higher one is declared the winner. Initially,players 1 and 2 compare their numbers; the winner then compares with player 3; and so on. Let X denote the number of times player 1 is a winner, and let Y = X + 1. Express the following quantities in terms of n.
$P[Y = i]$ and $P[Y\geq i]$ for $i = 1,..,n$
I really have a hard time with problems such as these and would appreciate any tips on how to go about solving such questions. My initial intuition says that maybe a geometric or negetive binomial distribution is the way to go but I am not sure how to proceed.
Thank you for any help.