In a match between A and B probability of winning A is 1/2 and B winning is 1/3 and probability of draw is 1/6. Person who wins two consecutive matches will win the game. Find probability that A wins the game
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A wins if he wins the first game (probability ???) or the first is a draw and he wins the second (probability ???) or there are two draws and he wins the third (probability ???) or .... You should see a pattern if you write down the calculation for the first three.
There is an easier way. You can just ignore the draws and ask for the probability that A wins given that there is no draw. What is the chance A wins a decisive game?
Ross Millikan
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The question is worded poorly (I'm not sure I get the distinction between "match" and "game"), but it does say that A needs to win two consecutive matches in order to be the winner. So this isn't really an exact duplicate of the cited question; maybe it can be transformed into that question? – Nov 10 '17 at 17:39