$[8]$ Consider a $1-$period binomial model with $T=1$ and assume the risk free interest rate $r=0.$ That is$,$ the stock $($currently priced at $S_0=10)$ can got up to $S_T^u=u{S}_0$ with probability $p^u$ or down to $S_T^d=d{S}_0$ with probability $1-p^u$ where $p^{u}in(0,1).$ We know that $)=B_T=(1$