I have this Markov chain for a set of states, there are the outgoing and the incoming probabilities, it's an exercise, the teacher told us to check that the outgoing probabilities ($p_m^{out}=\sum_n p_{mn}$) for each state are correctly normalized, but he also asked us to calculate the sum of the incoming probabilities ($p^{in}$), and there are two elements for which the sum of the $p^{in}$'s is greater than 1 ($A_3$ and $A_4$), then the average $p^{in}$ (which he asked us to calculate as well) is also greater than 1, what does it mean? or what am I doing wrong?
Thank you in advance.