Suppose an island lies in the monsoon zone, and has just two seasons: Wet and Dry. The wet season lasts for 1/3 of the year, and the dry season for 2/3 of the year. During the Wet season, the probability that it is raining is 4/5; during the Dry season, the probability that it is raining is 1/4. Suppose I visit this island on a random day, and it is raining when I arrive. What is the probability it will be raining when I return to this island in a year's time? (You may assume that in a year's time the season will be the same as today but, given the season, whether or not it is raining is independent of today's weather.)
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Sep 13, 2020EXPERT
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