1. Suppose your friend Dan wants to bet whether it will rain tomorrow. He offers you 3:1 odds that it will rain tomorrow (that is, he will give you $3 per dollar you bet if it rains tomorrow). Your friend Samantha also wants to make this bet with you, but she offers you 5:4 odds that it will not rain tomorrow. Assume you have $100 to bet and that your own weather model predicts it will rain tomorrow with probability 0.1. (a) Assuming you bet $r with Dan and the rest with Samantha, find your expected earnings, as- suming your model is accurate. (b) What is the most you should bet with Dan if you want to make a positive profit