Suppose that you have a stock in the one-period binomial model with fixed u, d, and r such that 0 < d < 1 + r < u. Suppose that there are positive numbers p1 and q1 such that p1, q1 < 1, p1 + q1 = 1, and (1 + r)S0 = p1S1(H) + q1S1(T). Show that p1 = p and q1 = q. Hint: You know that the risk-neutral probabilities satisfy these equations as well.