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Question: Jane Delavan ran against Jeremy Bryson for state senate. In one precinct, one of the two voting machines did not work, and 227 votes were cast on the broken machine. Jane needed 139 of those 227 votes to win the election. On the other machine in the precinct, Jane received 51% of the votes. Since assignment of voters to ballot boxes is independent, what is the probability that Jane won the election?

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