Sammy the Seahawk is leading the Broward College (BC) Math Team in a competition against the Technical Higher Education of Mathematics (THEM). This competition consists of up to five rounds and the team that wins three rounds first wins the competition. The first round will be at BC, the second round at THEM, and the other rounds will continue to alternate locations. Sammy calculates that the probability of winning a round at BC is 0.7 and the probability of winning a round at THEM is 0.4. What is the probability that BC wins the competition? Your answer must be accurate to 5 decimal places.

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