c) Given that today is rainy, what is the probability that it will be cloudy the day after tomorrow? (d) Drought will be declared if it has not been raining for 3 consecutive days. What is the probability of having a drought on the 3rd day if there is no rain today?
part C D
Q.3 Suppose we categorize weather in Johor Bahru into 3 namely S1 = Dry, S2 = Cloudy,
and S3 = Rainy. Suppose also that based on our observation for the past 60 days, we
are able to come up with the following probabilities for these 3 kinds of weather as
shown in the Table Q.3 below. This table gives the probability of tomorrow’s weather
based on today’s weather. As an example, if today is dry, then the probability that
tomorrow will also be dry will be 0.7. Using this table, predict the following:
(a) What is the probability that tomorrow will be rainy given that today is cloudy?
(b) Given that today is dry, what is the probability that tomorrow is dry and the day
after is rainy?
(c) Given that today is rainy, what is the probability that it will be cloudy the day
after tomorrow?
(d) Drought will be declared if it has not been raining for 3 consecutive days. What
is the probability of having a drought on the 3rd day if there is no rain today?
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