A stock price is currently $$110.$ Over each of the next two six$-$month periods, it will either increase by $14\%$ or decrease by $8\%.$ The risk$-$free interest rate is $4\%$ per annum with continuous compounding.

$1)$ To use the $2-$step binomial tree model to calculate a option price on the stock, calculate p $($the risk$-$neutral probability$)$ for each step $($a six$-$month period$).2)$ What is the value of a one$-$year European call option with a strike price of $$110?$ Use no$-$arbitrage arguments $3)$ What is the value of a one$-$year American put option with a strike price of $$112?$ Use no$-$arbitrage arguments and the two$-$step binomial model.