A realtor who takes the listing on a house to be sold knows that she will spend

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A realtor who takes the listing on a house to be sold knows that she will spend \(\$ 800\) trying to sell the house. If she sells it herself, she will earn \(6 \%\) of the selling price. If another realtor sells a house from her list, the first realtor will earn only \(3 \%\) of the price. If the house remains unsold after 6 months, she will lose the listing. Suppose that the probabilities are as follows:

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What is the expected profit from listing a \(\$ 185,000\) house?

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