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in Applications of Matrices and Determinants by (46.9k points)
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Two newspapers A and B are published in a city. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after two years.

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Best answer

Let the present shares of A and B be denoted by (0.15 0.85) 

The transition probability matrix is given by 

Hence their market shares after 2 years will be 0.546 × 100 = 54.6 % and 0.454 × 100 = 45.4%

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