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prob of A winning series (adv prob)


jd-

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Hi im new to this forum cause im desperate for help :(

 

I have a question that goes like this :

 

2 players play a series of independent games in which A has probability p, B has probability q = 1-p of winning each game. A needs m games to win the series and B needs n more games to win the series. What is the probability of A winning the series?

 

I have come up with a half-solution so far but i dont know how to expand/simplify.

 

(fixing number of games p has to win =m, variable number of games that q wins=i)

 

http://www.junde.howtofish.net/proj/images/summation.jpg

 

 

Many Thanks!

jd

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