I have problems with solving the following problem. Can anyone give me a hint how to solve it? Thanks in advance!
Consider a contract that at time N will be worth either 100 or 0: Let S(n) be its price at time 0 < n < N: If S(n) is a martingale, and S(0) = 47; then what is the probability that the contract will be worth 100 at time N?
Hint: The expected value of the contract at time $N$ will be $47$ because of the value sequence being a martingale. But also we know that the actual value at time $N$ will either be $0$ or $100$. There is only one way to assign the probabilities for $S(N)$ being $0$ or $100$ so as to satisfy the expected value condition.