Practice FT2 Q8 - Looking for a detailed, worked solution with theoretical explanation

Charlotte the cat is either in the sunroom or garden. - If Charlotte the cat is cunently in the sunroom then she will spend her next hour in the sunroom with probability U10 or move to the garden with probability 31,311]. . If Charlotte the cat is cunently in the garden then she will spend her next hour in the sunroom with probability 4f5 or stay in the garden with probability lf. The movements of Charlotte the cat can be represented by a matn'x: A _ ( U10 4;!) ) _ 3:10 1 f5 ' a} if Charlotte the cat is currently in the garden, what is the probability that she moves to the sunroom in the next hour? Enter your answer in the box below. Give your answer to part {a} as a rational number. For instance, if your answer is 1 then write 1:3 3 lam b} Let p1 be the probability that Charlotte the cat is in the sunroom, p2 be the probability that she is in the garden. Find the VEDIEIIt V _ ( 1) suchthatltitilr 2? andpl +312 2 1. Give your answer to part {b} as a vector in Maple syntax. For instance, if your answer is then enter {1:3, 2:\" 3:: v= Ino c] Charlotte the cat is currentlyr in the garden. Use your answer to part {b} to determine the probabiitiy that she was in the garden in the previous hour? Enter your answer in the box below. Give your answer to part {c} as a rational number. For instance, if your answer is 1 then wn'te 1f 3 3