To see the equivalence of the two ways of determining option price in the example discussed here, we first work out the probabilities of a rise to $200 and fall to $50 that would make the expected return on the stock equal to the riskless rate of interest of 5 percent (these probabilities are what are called the "martingale probabilities"). Let the probability of a rise to $200 bep; the probability of a fall to $50 is thus 1 - p. The initial stock price is $100, so if the stock's expected return is 5 percent, the expected value of its price after a year must be $105. Hence, 200p + 50 (1 -p) = 105 and p = 55/150.

Donald MacKenzie, An Engine, Not a Camera, loc. 1284