Phil Dunphy, a real estate agent, is considering whether he should list an unusual $903,412 house for sale. If he lists it, he will need to spend $4,945 in advertising, staging, and fresh cookies. The current owner has given Phil 6 months to sell the house. If he sells it, he will receive a commission of $18,567. If he is unable to sell the house, he will lose the listing and his expenses. Phil estimates the probability of selling this house in 6 months to be 45%. What is the expected profit on this listing?

Expected Profit on the listing = $3,410.15

Step-by-step explanation:

Expected value is given by

E(X) = Σxᵢpᵢ

xᵢ = Each variable in the distribution

pᵢ = Probability of each distribution

So, we analyze the two possibilities now.

Phil's profit if he sells the house in the next 6 months

= (Commision - Expenses) = 18,567 - 4,945 = $13,622

Probability of this happening = 45% = 0.45

Phil's profit (or more appropriately, his loss) if he fails to sell the house in the next 6 months = (0 - Expenses) = 0 - 4,945 = -$4,945

Probability that he fails to sell the house in the next 6 months =

1 - (Probability that he sells the house in the next 6 months)

= 1 - 0.45 = 0.55

Expected profit = (13,622×0.45) + (-4,945×0.55) = 6,129.9 - 2,719.75

= $3,410.15

Hope this Helps!!!

.25

step-by-step explanation:

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