A call option on a stock is trading for $$30$ per share with a $$32$ exercise price. The stock's standard deviation is $36\%$ per year; the option matures in $6$ months; and the risk$-$free interest rate is $4\%$ per year.

a$)$ Find the risk neutral probability assuming $3$ months for each step.

b$)$ Find the call price

c$)$ Find the put price?