Question 1:

I have the following table:

Outcome__Odds

1________1

2________2

3________5

One may choose any pair of outcomes, i <not equal> j and bet that the outcome will be either i or j. What should the odds be on these three bets if an arbitrage opportunity is to be avoided?

Question 2:

I have a stock that costs 100. At a cost of C per share, I can purchase at time 0 the opportunity to buy the stock at time 1 for the price of 150. At time 1, it can either be 50, 100, or 200. Use the arbitrage theorem to find an interval for which there is no arbitrage if C lies in that interval.