first fiddler's bank has foreclosed on a home mortgage and is selling the house at an auction. There are three bidders for the house, Jesse, Sheila, and Elise. First Fiddler's does not know the willingness to pay of any of these bidders but on the basis of its previous experience believes that each of them has a probability of 1/3 valuing the house at $700,000, a probability of 1/3 valuing the house at $500,000 and a probability of 1.4 of valuing it at $200,000. First Fiddler's believes that these probabilities are independent between buyers. If first fiddler's sells the house by the means of a second-bidder sealed-bid auction (Vickery Auction), what will the bank's expected revenue from the sale be?

The answer is $474,074, but I do not know how to solve for it. Please help!