Answer Happy

According to historians, weather in the land of Oz has always
been as is now. People living in the land of Oz will never have two
consecutive days with snow. If they have a day with snow then one
quarter of the time the weather will change to nice weather the
next day, or else it will change to rain. There is a 20% chance
that a rainy day will be followed by snow, else, there is equal
probability of changing to either nice weather or continue with
rain. If they have nice weather on any day, half of the time it
will change to rain in the next, or else, it will change to either
snow or stay with nice weather with equal probability. Assume that
the weather conditions in the land of Oz meet the Markovian
property.
(a)In the average long run, how many days in a 20 days period
will the land of Oz have rain? (6 pts)
(b)Assume that on Tuesday there is a probability of snow of 0.35
and a probability of nice weather of 0.15, what is the probability
that the land of Oz will have rain on Saturday? (10 pts)
(Four decimals)
(c)How long (on the average) should people wait for nice weather
when they are on a snowy day? (9 pts)