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In a holiday gathering, two families: family 1 and family 2 play a game repeatedly and independently until one of them win. A given game

In a holiday gathering, two families: family 1 and family 2 play a game repeatedly and independently until one of them win. A given game ends in a tie with probability of 0.2. The probability that family 1 wins an individual game is 0.35, while probability that family 2 wins an individual game is 0.45. What is the probability that family 1 is eventual winner.

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