2.II.10F

$A$ and $B$ play a series of games. The games are independent, and each is won by $A$ with probability $p$ and by $B$ with probability $1-p$. The players stop when the number of wins by one player is three greater than the number of wins by the other player. The player with the greater number of wins is then declared overall winner.

(i) Find the probability that exactly 5 games are played.

(ii) Find the probability that $A$ is the overall winner.

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