A “bear” market is a time when, in general, the value of stocks on the stock market is going down. A “bull” market is a time when, in general, the value of stocks on the stock market is going up. Over the past 50 years, approximately one out of every four years has a bear market. It is difficult or impossible for anyone to reliably predict what the stock market will do next year. In light of that information, Hadrian runs a real estate company. If he buys the commercial property and a bull market happens he will probably get a profit of $500 000 over the next year. However, if he buys the commercial property and there is a bear market he will lose $300 000. If instead, he buys a residential building he expects a profit of $300 000 if there is a bull market or a profit of $100 000 if there is a bear market.

Alternatively, suppose that next year Hadrian tells you that he chose which policy to follow by flipping a coin! That would mean he chose at random, with a 50% chance of buying commercial property and a 50% chance of buying a residential property. He also tells you that he did not lose money last year. What confidence should you have that there was a bull market last year? Show your calculations, and explain your answer in not more than two sentences.