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Alex works at a movie theatre and he notices that summer movie attendance is affected by the weather. On any day during the summer, there is a 0.37 probability of rain. On rainy days, the probability that the theatre is full is 0.8. On sunny days, there is a 0.45 probability that the theatre is full. If the movie theater is full today, what is the probability that it rained, to the nearest whole percent?

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