Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S9 / 3 / 3

At strike $K=108$, the European put payoff is $(108-S_3{)}^{+}$. In the ascending-price order $72.9,89.1,108.9,133.1$, its values areRisk-neutral expectation discounted for three steps givesThe physical probability $p$ drops out because the complete two-state tree admits a replicating hedge. The strike is $108$, so the $108.9$ endpoint is out of the money; replacing it by a positive payoff would materially change the price.