1. Bob likes the chances of Seattle against the Chargers. He is willing to give 3:2 odds.
Sue also likes Seattle against the Chargers. She thinks 1:2 odds constitute a fair bet with her betting on the Chargers.
To explain, she is will to bet the Charges will win where for every two dollars you bet with her, she will return 1 dollar if Seattle wins. (Or, if you were willing to bet where she supports Seattle, she will give the opposite odds -- if the Chargers win, she will give 2 dollars for every one dollar bet with her.)
a) Determine whether there is an arbitrage opportunity. Explain why or why not.
b) Now, I happen to think that the Chargers have a chance to win, particular with the odds. I have $100. Here is the situation: if I bet $100 with Bob and if the Chargers win, I will win $150, That is the good news. The bad news is that if Seattle wins, I will lose $100.So, a different strategy is for me to bet on the Chargers with Bob, and on Seattle with Sue as a hedge--it is a hedge because if Seattle wins, I will lose money to Bob, but some of the winnings from Sue will cover the hurt.
How much should I bet with each to minimize my losses if Seattle wins? How much would I win if the Chargers win?
2. Nancy is willing to give a to b odds that it will rain on Saturday. She finds this to be a fair bet.
What is the probability that Nancy assigns to it raining on Saturday?