A stock is currently selling for $50.$ The risk free rate is $5\%.$ The price of the stock will either be $55$ or $40$ in one period. The option strike price is $50.$

a$)$ Find the $\backslash$Delta $?$

b$)$ What is the value of a call option on $1$ share of stock?

c$)$ If the stock price range becomes $60$ and $40,$ what will happen to the price of a call option? What about

a put option?