Selling the Farm

Two competing companies are trying to buy up all the farms in a certain area to build houses. In each year 10% of farmers sell to company 1, 20% sell to company 2, and 70% keep farming. Neither company ever sells any of the farms that they own. Eventually all of the farms will be sold. Assuming that there are a large number of farms initially,  what fraction do you expect  will be owned by company 1 ?

 

 

 

[Durrett “Elementary Probability”, p 159 # 39]

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