Phil Dunphy, a real estate agent, is considering whether he should list an unusual $886,377 house for sale. If he lists it, he will need to spend $4,961 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 $15,342. 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 41%. What is the expected profit on this listing?

Question

Phil Dunphy, a real estate agent, is considering whether he should list an unusual $886,377 house for sale.  If he lists it, he will need to spend $4,961 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 $15,342.  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 41%.  What is the expected profit on this listing?