(A generalization of Problem 26) $A$ and $B$ are playing a sequence of games. For each play, each have an equal change of winning. The first person who wins $n$ plays will be the winner of the game. Assume that $A$ has already won $i$ plays and $B$ has already won $j$ plays. Let $E$ denote the probability that $A$ will win the game. (a) Express $P(E)$ in terms of $n, i$, and $j$. (b) Verify the results obtained in Problem 26 using the expression for $P(E)$.