A supertn:ll"ket >ells three brands of baking powder. Of

Chapter , Problem 31

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A supertn:ll"ket >ells three brands of baking powder. Of those who bought bmnd A last. 70'-t will buy brand A the next time !hey buy baking powder. IO'l \\ill buy bmnd B . and 20'k "ill buy bmnd C. Of 1ho,e "ho bought brand B last. IW will buy bmnd A the next time they buy baking powder. 60~ will buy brand B. and 3W will buy brand C. Of those" ho bought bmnd C last. IO'k will buy each of brand~ A and B the next time they buy b:~ing po" der . and 80'l: will buy bmnd C. (a) Assuming that the infom1ation describes a Markov chain. write a tr:.msition matrix for this situation. (b) If a customer la>t bought brand B. what is the probability that his or her next purchase of baking powder is brand B? (c) If a customer la>l bought brand A. what is the probability that hi> or her >ccond future purchase of baking powder is brand C? (d) Over the long run. what proportion of the s upermar ket' baking powder >ales arc :1ccounted for by e