Suppose you are an art dealer. You specialize in buying paintings by unknown painters at auctions and re-selling them to museums and art galleries. Since the painter is unknown, the cost of a painting is $1000 on average (you can assume that this is a fixed, constant cost of a painting). When you buy the painting, you thoroughly inspect it in your lab to try to determine if the painter is known.
You have been doing this job for 15 years, and you have determined from past data that there is a 0.25 probability that a painting is from a known painter, in which case you can sell it for $3,750 to a
Museum. If the painting is not from a known painter, you are only able to sell it to a gallery for $300. Suppose you buy 7 paintings at the auction.
What is the probability that you make a positive net profit off those 7 paintings?