In the state of Campana, during the Fall season, it rains 75% of the time and it is sunny 25% of the time (these figures are based on historical data). The local weather service every day announces either “Fair” or “Bad”. In the past, 75% of all the sunny days were preceded (the day before) by an announcement of “Fair” by local weather service and 50% of the rainy days were preceded by an announcement of “Bad”.

Question

In the state of Campana, during the Fall season, it rains 75% of the time and it is sunny 25% of the time (these figures are based on historical data). The local weather service every day announces either “Fair” or “Bad”. In the past, 75% of all the sunny days were preceded (the day before) by an announcement of “Fair” by local weather service and 50% of the rainy days were preceded by an announcement of “Bad”.
(a) Suppose that today the local weather service announces “Fair”. What is the probability that it will be sunny tomorrow?
(b) Suppose that today the local weather service announces “Bad”. What is the probability that it will rain tomorrow?

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