Consider the asset with a current value of $100$ kr that is described by the $2-$step Binomial model depicted below. Assume that the continuously compounded dividend yield is $0\%$ per annum, and the continuously compounded risk free interest rate is $18\%$ per annum for all maturities. Consider an out$-$of$-$the$-$money put option with a strike price of K$=95$ kr on this asset that matures in $9$ months.

a$)$ Calculate the risk neutral probability that the stock price will increase from $$100$ to $$156\mathrm{.}25$ in $9$ months.

b$)$ Calculate today's value of the option assuming that the option is of European type. c$)$ Calculate today's value of the option assuming that the option is of American type.