You are attempting to value a put option with an exercise price of $$110$ and one year to expiration. The underlying stock pays no dividends, its current price is $$110,$ and you believe it has a $50\%$ chance of increasing to $$120$ and a $50\%$ chance of decreasing to $$80.$ The risk$-$free rate of interest is $12\%.$

Required:

What will be the payoff to the put, Pu$,$ if the stock goes up$?$

What will be the payoff, Pd$,$ if the stock price falls?

What is the weighted average value of the pay off?