In a city, every day is either cloudy or sunny (not both). If it's sunny on any given day, then the probability that the next day will be sunny is 3/4. If it's cloudy on any given day, then the probability that the next day will be cloudy is 2/3.
a) In the long run, what fraction of days are sunny?
b) Given that a consecutive Saturday and Sunday had the same weather in the city, what is the probability that that weather was sunny?
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