A painting has a 20% chance of being real and an 80% chance of being fake. If it's fake, you can sell it for $10,000; if it's real, it's worth $500,000. 1. What is the expected value of the painting? 2. If you could buy the option to purchase the painting for $100,000 after learning whether it is real or fake (but are not obligated to buy), what is the value of this option?