Problem 9 You have a box with 4 coins, all weighted. It is given that: 1 coin comes up heads with probability 0.1 (Category 1). 1 coin comes up heads with probability 0.5 (Category 2). 2 coins come up heads with probability 0.8 (Category 3). 1. Someone offers you the following bet: You will take a coin at random out of the box and ip it. If it comes up heads, he pays you $10; if it comes up tails, you pay him $10. Should you take the bet? What is your expected prot (positive) or loss (negative) if you take the bet? Draw the decision tree, including the decision whether to take or reject the bet. 2. The other person now gives you a third option. You will pull a coin at random out of the box. You can ip the coin once, to test it; however, he will charge you $1 for that. When you see the outcome, you have a choice: You can quit, in which case the game is over, or you can ip the coin, in which case he will pay you $10 if it is heads and you will pay him $10 if it is tails. What, now, is your best strategy? What is your expected prot or loss if you follow your best strategy? Draw the decision tree