Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.6. If it rains, it will be sunny the next day with probability 0.5. Answer the following questions: 1. What is the probability that it will rain the next day if it was sunny the previous day? 0.4 2. Suppose that the weatherman estimates there is a 90% chance of showers today. Find the probability vector representing this estimation where the state 1 is sunny and state 2 is rainy. .1 .9 3. Based on the meteorologist's estimation, what is the chance of rain tomorrow?

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