Please help find a strategy to solve (iii) and (iv) below.

Consider an urn containing 5 rod balls and :1 blue balls. Two players A and H play a game as follows: in round 1, player A pinks 3 balls at random from the urn, notm the colors, and return th to the urn. In round 2, player H pinks 3 balls at random, notes the mlors, and then return them back to the urn, and so on. A's objective is to obtain 3 red balls, and H's objective is to obtain 2 red balls and 1 blue ball. If a player reaches his or her objective at one round, the game ends (therefore, the game can end in the rst, second, third, etc. round]. [i] [5 points} Find the probability that A picks a winning set of balls at a round. Find the probability that H pinks a winning set of balls at a round. [ii] l? points} Find the probability that A wins the game, that is, he is the rst to win a round. Hint: For this and the next question you may want to derive a recursive formula. (iii) [ii points] Find the expected number of rounds played until one player wins. [iv] [5 points] Assume that the game changm as follows: at each round, player A picks 1 ball and notes the color, then, without returning the ball back to the urn, player B picks a. ball and notm the color, then without returning the ball, player A picks another ball, and so on until both players have picked 3 balls. Assume the players have the same objective as before. Similar to [i] above, nd the probability that A and the probability that B pick a winning set of balls at a round. Hint: We are only concerned about a single round. Don't be shy to dive into oombinatories for this one