(Solved): Sam thinks the Leafs have a real shot at the playoffs next year. In fact she regards the following ...

Sam thinks the Leafs have a real shot at the playoffs next year. In fact she regards the following deal as fair: if the Leafs make the playoffs, you pay her \( \$ 2 \), otherwise she pays you \( \$ 10 \). Suppose Sam equates money with utility: for her, the utility of gaining \( \$ 2 \) is 2, the utility of losing \( \$ 10 \) is \( -10 \), and so on. Sam also thinks the Leafs might even have a shot at winning the Stanley Cup. She's willing to pay you \( \$ 1 \) if they don't win the Cup, if you agree to pay her \( \$ 2 \) if they do. That's a fair deal for her. What is Sam's personal conditional probability that the Leafs will win the Stanley Cup if they make the playoffs? (Assume that winning the Stanley Cup logically entails making the playoffs.)