\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A library studies the borrowing habits of its users between three categories: Fiction (F), Non-Fiction (N), and Comics (C).
  • 70\(\pourcent\) of Fiction readers choose Fiction again the following week, 20\(\pourcent\) switch to Non-Fiction, and the rest choose Comics.
  • 60\(\pourcent\) of Non-Fiction readers choose Non-Fiction again, 30\(\pourcent\) switch to Fiction, and the rest choose Comics.
  • 50\(\pourcent\) of Comics readers choose Comics again, while the remaining 50\(\pourcent\) are equally likely to switch to Fiction or Non-Fiction.
Using the order \((F, N, C)\), write the transition matrix \(\mathbf{M}\) for this Markov chain.
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.