Recently, a market research team has conducted a survey of consumer buying habits with respect to three brands of talcum powder in an area. It estimates that, at present, 20 per cent of the customers buy brand A, 50 per cent of the customers buy brand Band 30 per cent of them buy brand C. In addition, the firm has analysed its survey data and has determined the following brand switching matrix:

What will be the expected distribution of customers two time periods later?

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Brand Next Bought Brand Just Bought A B A 0.6 0.3 0.1 B 0.4 0.5 0.1 C 0.2 0.1 0.7