A European binary put option has a payoff of $1 when the option is in the money (K >= ST) and a payoff of $0 when the option is out of the money (K < ST). Using the following data, find the price of the binary put (recall that you can use risk-neutral probabilities to price any type of option, not just standard calls and puts). Use a two-step tree.

K $21 M (years) 1 S₀ $20 r 3.0% u 1.2 d 0.8