3. An investor acquires the stock for $11,000 and the put option for p dollars (with a strike price of $10,000 after one year), and the stock price is expected to rise to $12,000 with probability 91 or fall to $9,000 with probability q2 after one year (where q + q2 = 1). 3-1) Find the current put option price, p, and the probabilities of the stock price increasing, 91 , and decreasing, 92, such that the expected returns of the stock and put option after one year are 0, and b, respectively. (Hint: Construct a 2x3 state-reward matrix with the probability constraint q + q2 = 1 enforced in the last row of the matrix and a 2x1 vector with q and 92). 3-2) When the put option price p increases, how does b changes? 3-3) Find the condition under which arbitrage does not occur in (3-2).