A certain party takes place in two rooms: the living room (A) and the kitchen (B). After every 15 minutes, each person at the party decides whether to move to a different room or leave the party (C). If any given party-goer is in the living room, then she will stay in the living room with a 95 percent probability or move to the kitchen with a 5 percent probability. If a party-goer is in the kitchen, then she will stay in the kitchen with a 50 percent probability, move to the living room with a 40 percent probability, or leave the party with a 10 percent probability. If a party-goer has left the party, she may return to the living room with a certain probability or never return (that is, stay in state C) with a probability of 99 percent. Find the stochastic matrix governing the movements of the party-goers. Find the steady state vector. Explain what the steady state vector means for the party-goers. If 80 percent of the people are in the living room and 20 percent of the people are in the kitchen at a given time, where are the people half an hour later? I am asking for the percentages of each; what percentage of people are at A, B, C?

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