Consider a one$-$step binomial tree on stock with a current price of $$60$ that can go either up to $$70$ or down to $$50$ in $1$ year. The stock does not pay dividend and interest rates are zero. We want to price the $1-$year $$65-$strike European put option on this tree. $($i$)$ What's the put option payoff $1$ year later if the stock price ends up at $$70?$

$($integer$)$

$($ii$)$ What's the payoff if the stock price ends at $$50?($integer$)$

$($iii$)$ Use the tree to compute the value

decimal$)$ and delta $(2$ decimals'

going up to the $$70$ mode of the tree? $(2$ decimals$)($Write all answers in the exact required decimals.$)$