# Sunny Days in Mathtown

The weather in Mathtown behaves strangely. On each day during the month of March, it is either sunny or raining. If it was sunny on a particular day, it will be sunny the next day with probability $$\frac{9}{10}$$. If it was rainy on a particular day, it will be rainy the next day with probability $$\frac{7}{10}$$. Suppose the probability that it is sunny on March $$1^{\mbox{st}}$$ is $$p$$ and that the probability of it being sunny on any given day during the month is identically $$p$$. Then $$p$$ can be expressed as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a + b$$?

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