TOPIC: MARKOV CHAINS

A housewife always uses one of three brands of detergent: "A", "B" or "C". Which one she buys depends in which of the three manufacturers is running a promotional campaign (with gifts such as combs, ornaments, etc.), etc.). Companies undertake such campaigns at random, regardless of whether or not competitors are running other campaigns at the same time. not running other campaigns at the same time. Brand "A" company runs a campaign of the time, brand "B" runs a campaign 1/3 of the time, and brand "B" runs a campaign 1/3 of the time, and brand "C" runs a campaign 1/3 of the time. 1/3 of the time, and "C" promotes 1/3 of the time. If the lady buys brand "A" on a certain occasion, the next time she will also buy brand "A". If she buys brand "A" on a certain occasion, the next time she will also buy brand "A", if your company is promoting or if neither of the other two is doing so. or she buys brand "B" if it is on promotion, but brand "A" is not, or she buys brand "C" if it is the only one on promotion. the only one in a promotional campaign. If the lady buys brand "B" on one occasion, the next time she will buy brand "A" if it is on promotion. she will buy brand "A" if it is the only one on promotion at that time, or she will buy brand "B" otherwise. If she buys brand "C" on a certain occasion, the next time he will buy brand "A" if it is the only one on promotion at that time, or brand "C" if it is the only one on promotion at that time, or brand "B" if it is the only one on promotion at that time. "C" if it is running a promotion, but "B" is not, or will buy "B" if it is not. In what proportion of the time does the housewife buy each of the brands?