You are interested to value a put option with an exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it either increases to $120 or decreases to $80. The risk-free rate of interest is 10%. Calculate the put option's value using the binomial pricing model, presenting your calculations and explanations as follows:

a. Draw tree-diagrams to show the possible paths of the share price and put payoffs over one year period. (Note: Show the numbers that are known and use letter(s) for what is unknown in your diagrams.)

b. Compute the hedge ratio.

c. Find the put option price. Explain your calculations clearly.