Consider the call option where the initial price of the security is assumed to be 100. But, now suppose that the price at time 1 can be any of the values 50, 200, and 100. Suppose that we want to price an option to purchase the stock at time 1 for the fixed price of 150. For simplicity, let the interest rate r equal to zero. Show that no arbitrage is possible for any option cost in the interval [0, 50/3].