Problem 1.23 You play a match against an opponent in which at each point either you or he/she serves. If you serve you win the point with probability p,, but if your opponent serves you win the point with probability p2. There are two possible conventions for serving: (i) alternate serves; (ii) the player serving continues until he/she loses a point. You serve first and the first player to reach n points wins the match. Show that your probability of winning the match does not depend on the serving convention adopted.

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