Each of the two players A and B toss N fair coins. Let pi be the probability that i coins of the N coins player A (equivalently player B) tossed shows heads.
a) What is the probability the two players have the same number of heads? (You do not need to calculate pi.)
b) If the game is modified so that player A tosses N +1 coins (player B still tosses N coins), show that he probability that player A has more heads than player B is 0.5 .