(Solved): 8 finite math A large group of mice is kept in a cage having compartments \( A, B \), and \( C \). M ...

A large group of mice is kept in a cage having compartments \( A, B \), and \( C \). Mice in compartment A move to B with probability \( 0.3 \) and to \( C \) with probability 0.4. Mice in B move to \( A \) or \( C \) with probabilities \( 0.15 \) and \( 0.35 \), respectively. Mice in \( \mathrm{C} \) move to \( \mathrm{A} \) or \( \mathrm{B} \) with probabilities \( 0.4 \) and \( 0.4 \), respectively. Find the long-range prediction for the fraction of mice in each of the compartments. The long-range prediction for the fraction of mice is in compartment \( A \), in compartment B, and in compartment C. (Type integers or simplified fractions.)