The gt brewery has hired you as an analyst to understand its market position. it is particularly concerned about its major competitor, the ml brewery, and which brewery has the ‘lead’ market share. recent history has suggested that which brewery has the ‘lead market share’ can be modeled as a markov chain using three states: gt, ml, and other company (oc). data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data:
gt ml oc
gt 0.75 0.15 0.10
ml 0.30 0.60 0.10
oc 0.20 0.10 0.70

a. the current state of the lead market share in november is gt·the gt brewery is considering launching a new brand in march only if it has the lead market share in february. determine the probability that gt brewery will launch this new brand. show any equations or matrices used to calculate this probability and briefly explain how you obtained your answer.
b. provide the steady-state equations and calculate the steady-state probabilities for the markov chain.