So I defined a probability measure $Q$ on the probability space and set up a system of equations such that $s_o$ equals the expected discounted value of the time $1$ price and that the sum of the probabilities under $Q$ sum to $1$ and are nonzero. I end up with the condition $$r=uQ(\omega_u)+mQ(\omega_m)+dQ(\omega_d)$$. Aren't there an infinite number of solutions here? I'm stuck at this point. I've also looked at part $2$ and do not even know where to begin. Any help would be appreciated