John and Steve are participating in an online game.

The player who wins three rounds first is declared as the overall winner. Suppose that John is a better player with a probability of 0.7 for winning a game. Assume that the result of the game is independent from each of the game.

a. What is the probability that John will be declared the winner?

b. What is the probability that a fifth round will be needed to determine the winner?

c. If John has won the first round and Steve has won the next two rounds, i what is the probability that John will win the game?

ii what is the probability that a fifth round will be needed to determine the winner?