suppose there are only two weather states: sunny and raining. If
today is sunny, the probability of raining for tomorrow is 0.6. If today is raining, the
probability of sunny for tomorrow is 0.7. Based on climatic records, during a year of 365
2
days, the number of sunny days is 265 days on average, and the remaining days are raining.
Please do the following
(1) What is the probability of sunny for tomorrow given today is sunny?
(2) What is the probability of raining for tomorrow given today is raining?
(3) Given today is sunny, what is the probability that yesterday is sunny as well?