Logan works at the new landmark theatre, he is telling his friends how busy it is. He says that on any day during the winter, there is 0.37 probability of snow. On snowy days probability of the theatre being full is 0.8. On clear days, there is a 0.45 probability that the theatre is full. On clear days, there is 0.45 probability that the theatre is full.

Determine the probability that the theatre is quiet on the clear days in the winter.