Problem #3 An Interesting Coin Game Suppose that two people A and B are playing a game with a single coin which has probability p of coming up heads and q = 1 p of coming up tails. The game begins with A ipping the coin and then B ipping the coin and then A ipping the coin and then B ipping= and so on, until the coin comes up heads. The wimler of the game is the one that ips a heads on the coin. a.) The game is in no person's favor if the probability that A wins is the same as me prooaonity that B wins, both being 1f2. Show that the game is always in A's favor (ta. PM) > 1.2 and HE) 151} from the Casino. The game is called fair to a given player if the average winnings (per play) for that player is $0. Determine {in terms of c and p) the values of a and b if the game is to be fair to both players