Chapter 9.1, Problem 1ED

(A) Refer to the transition diagram in Figure 1. What is the probability that a person using brand A will switch to another brand when he or she runs out of toothpaste?

(B) Refer to transition probability matrix $P$. What is the probability that a person who is not using brand A will not switch to brand A when he or she runs out of toothpaste?

(C) In Figure $1$, the sum of the probabilities on the arrows leaving each state is $1$. Will this be true for any transition diagram? Explain your answer.

(D) In transition probability matrix $P$, the sum of the probabilities in each row is $1$. Will this be true for any transition probability matrix? Explain your answer.