Question: Shantanu is a huge baseball fan; he is very excited that the Red Sox won the 2007 World Series, so he decided to travel to Las Vegas to bet on the next Series.
For $100, he bought a certificate from a casino, which allows him to stake that $100 on whether the Red Sox will win the 2008 series. The casino is offering four-to-one odds for the Red Sox not to win a second time consecutively. That is, if Shantanu declares that the Red Sox will win, he will receive $500 if he is correct, and if he declares that they will not win, he will receive $125 if he is correct. In either case, if he is incorrect, he gets nothing.
Assume that to Shantanu, any dollar amount one year from now is worth as much as any dollar amount today. Suppose that Shantanu thinks that the Red Sox have a 40% chance of winning the 2008 Series and that the clairvoyant comes to Shantanu and offers to tell him who is going to win, for a fee. Assuming that Shantanu is risk neutral, in what range does his value of clairvoyance lie with respect to the deal he faces?
a. Greater than or equal to $0, but strictly less than $50.
b. Greater than or equal to $50, but strictly less than $100.
c. Greater than or equal to $ 100, but strictly less than $ 150.
d. Greater than or equal to $150.