The option to buy after inspection
A painting is an original with probability , in which case it is worth 500,000 dollars; otherwise it is a copy worth 10,000 dollars. After an inspection that reveals the truth, you have the right, but not the obligation, to buy it for 100,000 dollars.
How much is this right worth, in dollars?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
After the inspection, when do you buy?
The right pays , where is the painting's value.
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. This is a call option with strike 100,000 on the painting's value. You exercise only when the painting is an original.
Step 1. If the painting is an original, buying gains . If it is a copy, you do not buy: you gain 0.
Step 2.
Compare. Buying blind for 100,000 would be worth on average . The right to walk away after seeing the truth adds 72,000: the value of an option comes from avoiding the bad outcomes.