a little help with this probability problem

[jba]

ok it's actually two problems.

two players are playing a game. They will win with frequency X and Y. What is the probability after N games that player A will win P more games than player B?

for example:
player A will win 60% of the time
player B will win 55% of the time

what is the probability that B will win 5 more games than A after they each player 30?


The first question is how to calculate this if they are independent games (ie, player A and B can both win or lose any given game). The second question is how to calculate if they are dependent - ie, player A wins 60% and player B wins 40%, and if player A wins player B loses by definition and vice versa.


thanks!