You Are the Chief Appraiser for a Large Art Dealer

You are the chief appraiser for a large art dealer in a major American city. You are offered a chance to examine, and buy, a work of art. You have reason to believe that it is a piece from a famous artist of the 15th century that has been lost to the art world for hundreds of years. Such a painting would have an estimated market value of $1 million. However, you face two risks. First, the painting may be a forgery, a chance that you estimate to be .4. Second, even if the painting is authentic it may be stolen. Once you buy the painting, you bear all risk. If it is a fake, its value is $0. If it proves to be stolen (a .2 risk in your estimation), you must return the painting to its rightful owner and you cannot recover the purchase price.
(a) You have the chance to buy the painting for $500,000. As a risk-neutral decision maker, should you make the purchase?
(b) Suppose you can buy insurance against the risk of theft. You pay a premium of $20,000, and the insurance company compensates you according to your purchase price if the work proves to be stolen. Should you buy the painting for $500,000?