(Solved): Consider a simple three-state Markov model of the weather. Any given day, the weather can be descr ...

Consider a simple three-state Markov model of the weather. Any given day, the weather can be described as being: State 1: precipitation (rain or snow), State 2: Cloudy, State 3: Sunny. Transition between states is described in the figure below: Given that the weather on day \( t=1 \) is sunny, what is the probability that the weather for the next 7 days will be "sun, sun, rain, rain, sun, clouds, sun"? A. \( 0.01536 \) B. \( 0.1536 \) C. \( 0.0001536 \) D. \( 0.001536 \)