Consider the example from (the first part of) the previous example, where the spot price is S0 = $100. What is the probability that a 1- year butterfly made of European calls with strikes 90, 100 and 110 will have a payoff of $5 or less?

(the first part for reference):

Consider the model of a stock where it either goes up by 7% or down by 4% each year. Let p(up) be the probability that stock goes up and p(down) the probability that stock goes down.

(a) Suppose that p(up) = 52% and pdown = 48%. Recall the expected rate of return is defined as the number which satisfies the equation E[S1] = S0e ^(1) where S0 is the known asset spot price and S1 is the unknown asset price in one year from now. What is the expected rate of return of the stock?